I had this same problem in my 2010 JK (about same miles). It is intermittent. I had it had the dealer and asked them to look at it and they could not reproduce it (because it's intermittent). After that, it started doing it virtually all the time. Finally, I decided maybe there was bad fuse or bulb (even though the bulbs had been confirmed to be good twice) and stopped to buy some spares to change out.
Before I did change the bulbs, I decided to test one more time and this time my rear turn signal light was not working. I figured that must be the problem: a marginal bulb that finally went out. So I took off the cover and prepared to install a new bulb. Once I got in there and examined the bulb, it was obvious the bulb was fine. I tested the signal again and it worked fine-normal pace. So I put everything back together and it has worked correctly ever since. I've still got the spare bulbs, but so far have not needed them. I'm not sure if something was just loose (didn't look like it to me) but after taking the assembly apart and putting it back together everything has worked fine.
I'm not really sure what is going on, but short of changing out everything one part at a time I'm not sure I ever will know.