I don't think the turn signal switch is the problem. If you don't already have a 12 volt test light, invest a few $$ in one and you can isolate this pretty quickly.
One side of the stop light switch (on my '53 this is mounted on the firewall, just above the brake pedal rod)is always hot. Using your test light (or meter if you have one)find the hot side of the switch when the light switch is off. Turn the light switch on and see if that terminal is still hot. If not, the problem is in the lightswitch, if so, the problem is probably a poor ground back at the taillights.
