So I have an electrical gremlin in my 1998 XJ that comes and goes. When I put an electrical load on the system for example, rolling my window(s) up I have my radio cut out. When I roll my window up from being open I have no issue as the window is moving up, but when the window gets to the top and seats itself and the lights dim, that is when the radio temporarily cuts out. My battery is maybe 2 years old and I have never had a starting issue which makes me think/hope it isn't the alternator. I do have an aftermarket radio I could wire up and see if the issue persists?I hope my video works.

 

Bad grounds would be my guess start with the battery to frame and clean to bare metal, check cables also. Good a place as any to start your not getting a good solid contact somewhere.