Side light comes on when breaking

Sounds like a short between the brake light wiring and the side light wiring. This is most likely cause by rubbing causing the wires to become exposed.

Does this only happen this way or does turning on the headlights cause the brake light(s) to come on?

try checking All yer brake bulbs.

what happened to me awhile back was when
braking, the dash lights would come on??!?!?!

to me a few days to figure it out.
turned out to be a bad brake bulb that
the filament had bured out, fell down,
and contacted the other filament inside
the bulb....freaky..... :weirdo:

I've just rechecked all the other lights, and the following lamps do not appear to be working either:

OS Tail lamp
OS Stop lamp
OS Fog lamp