Give this a try.
Also, at any local auto parts store you can pick up a Haynes or Chilton manual that is a good starter guide to repairs on your Jeep.
Also, welcome to the JF. There is a wealth of information on here. Learn to use the "search" feature at the top of the screen.
And just in case someone hasn't told you, and even though you a CJ that is apparently in good shape......J.E.E.P. = Just Empty Every Pocket.
To try some fixes, pull each fuse, one by one and check them. Next check your light switch, it might actually be bad. Are the bulbs bad. Do the other "parking lamps" work when the headlights are turned on.
Welcome and have fun out there!
79 CJ7, 3" Lift, 360 V8, Edelbrock Performer Intake, Comp Cam, Holley 650 Truck Avenger, Hedman Headers, Moser Axles, Herculiner, Warn M8000i, 33" Timberlines
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