it's probably a trail squirrel that's gotten in there and is ****ing with you...
is it the stock stereo? it sounds like there's a wire or a switch worn out inside of the unit, i doubt this is going to be something fixable, and if it is, slim to no chance it would be worth your time to actually do it... go look for a replacement stereo
how much do you pay yourself? think about it this way, cost of getting a replacement stereo, and having someone install it in your truck, divided by the number of hours it would take you to remove, disassemble, diagnose the problem, fix, re assemble and reinstall...
around here, you're looking at probably $60 install and around $120 for a new decent good stereo, cheapies can be had for probably $60, and used for like 10$ or so at the pawn shop... you have to remember that your stereo isn't new, so you can't value it as a new stereo... so $70/ what 5-10 hours of labor for you to do all of that? lets say 7... that gives you 10$ an hour is what you're paying yourself for a massive headache... is it worth it?
and to top it off, it may not be a problem you can fix, so now you're paying yourself $60 for 7 hours of work (because stereo is garbage) or subtract the cost of replacement parts...
simply put, car stereos are cheap, they aren't worth repairing... they are disposable unless it's under warranty