Hey Jim,
I don't mean to talk down to ya or sound like an echo B-U-T, as Tony suggests, I'd be sure all is well with the bulb(s). I can't be the only guy that ever grabbed the wrong bulb. Or opened a NEW pack and somehow got the only BAD bulb. Or didn't insert it just "so." Or had a problem that I didn't even make myself.
Basically, I had the same type problem you describe with the '56 convertible I bought about a year ago. I called the previous owner and he said it had always been screwed up - for the 3 years he owned the car! (Oh KRAP, thought I!!)
Well, the good news is after half hour or so of screwing around with bulbs, making sure they were 'in' just so and etc. etc. ALL is fine. The turn signals and brake lights work properly whether the lights are on or off, etc. NO expensive / time consuming wiring hassle. Basically, just a damned bulb.
I hope this inspires you to try some of the simple stuff first. You know, kinda like KISS.
Like I said, I definitely do NOT mean to be talking down to ya.... just hoping the best for ya!
Bill.