I have no LEDs, nothing on that I can remember
Hmm. I'm stumped without being able to look at it but something isn't right. You might be able to live with it but don't. When I first got into ham radio I bought a terrible radio and didn't know it was terrible until I got a new one. I just thought it was normal and I was really frustrated with radio because of it.
Three simple ideas to try. Unscrew the coax from the back of the radio and see if it still makes that sound. That will eliminate the coax and antenna. You could also leave the coax connected and unscrew the antenna to eliminate the antenna.
Second idea, take the radio out of the mounting bracket and see if it still makes that sound. If the bracket is screwed into metal, it is likely acting as a second ground point for the radio (depending on how the radio is made). That's fine and probably isn't a problem, but it's something else that can be eliminated as a potential problem.
Third idea, did you say your dad got a cb too? Can you put his in your Jeep and see if it works? That will tell you if it's your radio or your Jeep. You could also put your radio in his vehicle or trade coax and antennas if that'll help pin down the problem.