If your left blinker is working okay, it's most likely your turn signal (multifunction) switch. If you are also having weird issues with other rear lights, pull the body bolts in your tail light fixtures and make sure they are providing a good ground.
Brysauce, forgot to welcome you to the forum, so Welcome! Your TJ is an amazing little vehicle. Keep it maintained and it will give you many years of good service. We have 2, 97 Sahara with 171K and 2000 Sport just rolled 194K.