It may be a loose connector on the back of the lighter assembly. It's not hard to remove. Start by removing the shifter boot chrome trim from the wood panel - carefully pry up on it with a soft wedge tool. Then remove the wood trim around the shifter - open the ashtray and then pull up firmly on the leading edge of that wood panel. After that, the entire ashtray component comes out. There are two plastic clips now exposed just under where the wood panel was. If you need photos, do a search for "radio installation" and these should be the first few steps of that process.
No need to remove the chrome trim ring. That puppy is plastic and the chrome cracks easily. Open you ashtray and you'll fell the seam at the front of the large piece the chrome ring is in. Easiest to put a small angled pry bar in there and pry up the front end of it. It then pulls forward and up. Then there are two small platic tabs that holdd the whole ashtray assmebly in.