Some more information after further attempts at testing potential sources of the problem:

• I checked the fuses on both the side panel and the relay panel and all appeared good, but I changed them out with new ones anyway
• I thought I'd had a magic repair as the fan came on when I started the car and AC after messing with the fuses and relay panel. But after buttoning up the lower dash and trying it again - no luck. Fan wouldn't run. But I did test it again by jumpering 12v power to the connector and it ran.
• I hooked up my multimeter to the "input" side of the fan connector coming from the fan control unit. Getting around 10.7 volts from it with: AC on, AC off, heater on - basically the signal didn't seem to change
• This seems to all point to the fan control unit. The question I have is, what voltage readings should I see coming out of that control unit to the fan? If it's a two speed fan, what causes it to change speeds? Is it a lower voltage for low speed and a higher voltage for high speed? Trying to find out what I should be seeing on my multimeter coming out of the fan connector fed from the control unit. Also, could my fan be the problem ie it should run on low speed with the 10.7 volts input, but isn't? But will run on high speed when fed 12 volts?

Appreciate any help.

Some additional info that might help others when tracking down similar problems:

1. The 2.8L V6 has a different setup vs the 1.8L - The V6 uses a coolant fan control module, which is on the "left frame rail bottom." The connector cable to the fan is coming from this module. It's circled in red in the picture
   
   
2. A pic of my relay panel highlights that there are no relays in the locations you'd see them on a 1.8L panel since this is handled by the coolant fan control module. To get to the relay panel you have to remove the lower dash panel that makes up the top of the drivers side footwell. There are 4 torx screws holding it in along with some clips.
3. The condenser / aux fan connector is the second one from the top on the plastic rack holding the connectors and located under the plastic cover around the power steering fluid tank top on front drivers side. It has two large wires connected to it (brown/black negative and red/black positive). The other connector has a lot more smaller diameter wires going into it. You can disconnect this connector and jumper 12v to the positive side and ground the negative, turn the car on, and see if the coolant fan will run. You can also put a multimeter into the other side of the connector to see what voltage is being sent by the fan control unit.
4. A diagram listing the relays in the panel above the drivers side footwell is posted on the Passat World B 5.5 Google Drive also listed under the B 5 Discussion Post VW Part Numbers (ETKA), diagrams, and general procedures !

 

AGGHHH... driving me crazy!! Tested the 4 pin coolant temperature sensor. The blue one connected down low in front on the passenger side. (Have seen other references to a temperature sensor that is toward the firewall behind the intake, so it's bit confusing).

Jumped pins 2 & 3 (numbering per this pin diagram so hope that's correct)

Started the car, turned AC on high, and Tah-Dah the condenser fan ran, AC compressor was engaged, cold air. But no so fast my friend.......

Repeated the process jumpering pins 1 & 4. No luck, the fan did not run, but the compressor was engaged.

Next step, disconnected the condenser fan connection and put my multimeter on the "input" side to see what voltages were coming in.
With pins 1 & 4 jumpered, and AC on high, I got 10.71 volts. With the AC turned to off, I got 10.94 v ?????

Switched the jumper back to pins 2 & 3, started the car and put AC on high. I got 10.59 v huh?????.

Put the fan power connector back together, and repeated my first test with pins 2 & 3 jumpered. This time, THE FAN DID NOT RUN ?!?!?!

BTW, with the car off, I got 9.82 v from the fan connector.

So now off to the Fan Control Unit. I still wish someone could lend a brother a hand here. In particular, what voltages should I see coming out of the fan power connector and how would that change for low speed vs high speed. Thus far, whenever the fan does run it appears to my eye to be the same speed. So don't know what the difference between low speed and high speed should look/sound llike

 

Started testing the coolant fan control module. Found a helpful thread on the topic here Auxiliary Fan Control Unit but the OP muttony clearly ended up dealing with much bigger challenges (I hope). In the post, FrescoGreen01.5 provided the following testing sequence, and I've included my results in italics:

1. Measure voltage on the 2-position connector (in harness) that plugs in to the Control Module. Should be 12V; if not, check 40A fuse. (You already did this step, included for completeness.) Passed, 12v on this connector with car off
2. Measure voltage between 6-position connector (in harness) pin 1 and ground. Should be 12V; if not check 5A fuse. Passed, 12v on this connector with car & AC running
3. Plug everything in except the fan, ignition off. Unplug thermal fan switch, jumper pins 2 & 3 (in harness connector). Your jumper is making the same connection the thermal switch (lower setpoint) does. Measure voltage on fan pigtail from module, should be 12V. You will probably hear the relay click in the module if it's quiet, too. Not sure, I measured 10.7 volts – would this be correct to get the fan to run at low speed?
4. Same conditions, jumper pins 1 & 4 in harness connector. This makes the same connection as the thermal switch (higher setpoint). Again, you should measure 12V on the fan pigtail (and hear relay click). If either this or the previous step fail, the module is bad. Not sure, I measured 10.7 volts – doesn’t seem to be correct to get the fan to run at high speed. Is there something else that would cause it to send a lower voltage when pins 1 & 4 on the thermal sensor are jumped?
5. If you measured 12V on the fan pigtail in the previous two steps, plug the fan in and repeat the two tests jumpering the thermal switch connector (keep fingers clear). The fan should run in low and high speed respectively. If not, replace the fan. Failed, plugged the fan back in with 1 & 4 jumpered, and then with 2 & 3 jumpered. Fan did not run in either case.

So it seems I am left with the following item to answer so I can decide what needs to be replaced. Is the issue:
A. The Auxiliary Fan Control unit is bad as it's not sending sufficient voltage to run the fan in either low or high mode
B. The condenser fan is bad as it won't run in low speed when provided voltage less than 12 volts
C. Some combination of both?

Pics:
Fan Control Unit mounted on front bottom of driver's side rail. Has three connectors: 1) Two wire pigtail that connects to the condenser fan near power steering reservoir 2) Two wire connector that provides 12 v positive & negative power from 40 amp fuse on relay panel 3) 6 pin connector that provides 1-12v power from 5 amp fuse on relay panel, 2)Not used 3)Control input to energize low speed relay inside the module 4) Not used 5)Control input for high speed relay inside the module 6) 12v output to after run coolant pump

Multimeter test showing 12 v power on connector to Fan Control Module

 

I wish I could help you, but I don't know enough about the running voltages apart from the fact that it sounds like the fan module is bad. Jumping the thermal switch should provide 12V to the fan, make sure the input to the module (the 2-wire connector from 40a fuse) is supplying 12V at the connector. Remove the connectors and check for corrosion. Also, check the battery connections and ground. I've seen bad battery connections with corrosion eating into the terminals that were not visible from the outside. Any large loads and the voltage would drop. My son's car had the ground stud next to the battery rust out.
Does the after-run coolant pump work?
Sorry if I seem scrambled, my meds screw with my thinking and memory.

 

Thanks for the response. Yes, getting 12v to the control unit module. Have not checked the after run coolant pump. Wish I had some way to test the fan for low speed operation. Any ideas on how to do that? About to the point where I'm just going to bite the bullet and replace the control unit - Parts Geek has one for $86. If that doesn't work, then will buy a new fan for another $50 and cross my fingers.

 

I don't know the voltages needed to run the fan at low speed or the resistance of the motor. I am very familiar with the wiring and location of everything as I swapped it all out on my old car.

 

So I went ahead and replaced the Cooling Fan Control Module with this one I got off Amazon for $92 URO Parts 8D0959501C Fan Control Unit Relatively straight forward to do with the exception of getting the two little 10mm nuts back on in the very tight space. Hooked it all back up and the fan didn't run. But I tapped it to start it turning and it started running a low speed. Jumpered the 1 & 4 pins on the temperature sensor and it reved up to high speed. Checked the voltage on the input to the fan connector from the control module and got 10.23 volts. So I guess that is about the voltage level that's sent to the fan to run at low speed. Am still worried that I have a problem with the fan motor itself since it appears it needs a nudge to get it started running in low speed. Any thoughts on such an issue where the fan will run fine at 12 volts, but not start at the lower voltage?

It's my son's car and I just told him he'll have to do it like the did in the old days when you crank started the car with a handle on the front; when you want the air conditioner to run, you'll need to open the hood and give the fan a sping to start it Will cross my fingers and see what happens before relenting to a fan replacement since that seems like a PITA due to the tight clearance.

 

Some electric motors are like that when they start to fail. It's why people whack starters to get them to work. I had a small heater fan that would only start on high, but then run on low just fine.