Turn signal switch is an easy repair, gotta pull the steering wheel though.
How did you guy's figure it was the turn signal switch? I would have never thought that either. It's odd because your turn signals DO work, but your brake and tail lights DO NOT.
My first thought was a bad brake switch, bad bulb or bad ground. I learned that even though a bulb lights, doesn't mean it works. I had a problem where when I turned on the left turn signal and it just stayed lit (didn't blink). Turns out it was the bulb. My Scamp had a dim right brake light, turns out that was a ground.
Only reason I replaced my turn signal switch was because the little arms were broken off and it didn't return after a turn.