I would agree that your switch is broken. I am a Jeep virgin (only owned my YJ for about a month) but I have run into this issue several times on motor homes that I have worked on.
You can buy a replacement switch at your local auto parts store, but in my experience they are poor quality and require several "tweaks" to make them work correctly, which is a royal pain considering you have to pull the steering wheel each time.
I would highly recommend getting a switch assembly from Shee-mar. Shee-Mar Home
They are complete replacement units that include the wiring harness with connector making them easy to install. No splicing wires etc. (at least thats been the case on the ones that I have purchased. You can check with them to see if this is the same for YJ switches) Hope that helps!