1994 Lesabre turn signals gone bad

This may be extremely easy for most of the experts out there, but since I have done so much mechanical intensive work on my car, I have no experience with it electrically. For some time, I have had trouble with my right turn signal and now the left has done the same thing. You know, where it comes on, but doesn't blink???? I replaced the bulb in the trunk compartment twice, and figured, ok, now it isn't that.....
What should I do? Where should I look? What are the possible issues that come with this, so I can go step by step on fixing this problem. Thank you all so much, once again, for all the input and expertise, as usual!

No blink means a bulb (or the wiring to a bulb) is bad. Try changing out any bulbs that are out. Next, try opening your trunk and swapping the wire harness and two outermost tail lights on each side and then retest. (Behind the gray trunk liner) I would guess that there is a short in your wiring harness connecting the right rear taillights. The lights connect in a Y shape and have a connector near that. You can disconnect them and swap the whole harness and two lights sockets with minimal effort. If your lights flash after swapping then get a new harness at a junk yard.

No blink means a bulb (or the wiring to a bulb) is bad. Try changing out any bulbs that are out. Next, try opening your trunk and swapping the wire harness and two outermost tail lights on each side and then retest. (Behind the gray trunk liner) I would guess that there is a short in your wiring harness connecting the right rear taillights. The lights connect in a Y shape and have a connector near that. You can disconnect them and swap the whole harness and two lights sockets with minimal effort. If your lights flash after swapping then get a new harness at a junk yard.
There is a new development with this issue. I have not yet had a chance to go messing around in my trunk compartment, but I had to do some trailer hauling this last weekend with a UHAUL. I did have a hitch and light kit installed years ago for my move from out of state since it would save me some money. Anyway, I noticed that when hooking it up and testing out the signals, they worked! What does this mean in the whole scheme of things??? Is there something wrong with the way that they hooked it up or spliced the wiring into my car that will only cause them to work with a trailer and not alone??? I was thinking about just getting another kit and just plugging one in to trick out my system just so I would have turn signals and keep from messing around with the wiring.......