Yes unplug cig lighter. Crap lighter socket can cause problems for radio and other things w/o blowing Bat fuse.
See my Cave,
Sneak Path and
LighterOld GM units will fail for several reasons...
Either/both plugs have problems. 2 pin has standby power to keep clock alive etc. rest and main power is on big plug. shown above.
After that any crack solder joint, 30+ year old caps and more in the "head" can kill them outright or be very intermittent. Even if you "fix" a problem somewhere else is still a problem.
Is part of why many vendors stopped selling most to all units w/ this plug setup. Even if they get working radios, they have to do more work to hope they work when installed. Example "Re-Capping" takes time and money and most don't want to spend for that.
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Dr. Ian Malcolm: Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.
(Jurassic Park)
The Ogre's Fiero Cave