Electric stuff can be a pain. What helps is a forum like this, a good cheap volt meter that is rated computer safe, and some test leads.
Get out your screwdrivers, remove, and check the bulbs by firing them off the battery directly with the test leads.
Use the volt meter to check which wire leads are sending the signal to the bulb. Then check the ground wire path to make sure it can conduct electricity from the inside of the bulb holder. Jeeps are known to lose ground right in the holder where you can't see it. So, no complete electrical pathway. Electricity has to come from the turn signal stuff to the bulb, through the filament, and back out to the fenderwell ground screws, or no circuit.
Of course, if nothing is clicking or blinking, it may be that - the "blinker." It sometimes goes bad when it runs out of fluid.
Just replace it with a known good one to check that.
All electrical parts are non-returnable at most stores, but this stuff doesn't run much.
"I feel your pain" about the electric gremlins, but with some experience, it comes around. I just built and installed a headlight wiring harness for some Hellas, scienced out my mistakes, and enjoy them. It came from stuff like here and replacing both turn signal holders in front.
