Just about anything is possible. I had a brakelight problem on my Motobecane, and it went like this:
Tail light was on all the time, and using either brake had no effect on the brightness. I checked the handlebar switches, and sure enough - one of them was not switching (they are the double-throw, 3-wire switches).
Took the switch off of the lever perch, and it fell apart in my hands. It was pretty tricky, but I was able to get it reassembled.. it was like working a little puzzle. After this, both switches worked fine, but I still wasn't getting a brake light.. or so I thought.
Pulled off the tail light lens, and tried it again. Turns out that when I applied a brake, the tail light filament was lighting - and the brake light was on all the time! I couldn't see this with the lens installed, as the brightness of the brake filament was masking the tail light filament.
So, I found that the wires to the brake light could be swapped. I switched them around, and that did it. Proper brake and tail light action.
This is one of those found-abandoned bikes, where everything is wrong. So, this wasn't too much of a suprise to me.