I get a "circuit failure" error when I try to use the cigarette lighter

Under normal circumstances, a cigarette lighter can be expected to draw roughly 10 amps, and cigarette lighter circuits usually have 10 or 15 ampfuses. This allows you to plug in phone chargers and other devices that draw less than 10 or 15 amps, depending on the fuse in your specific vehicle.

door locks and cig lighter ARE NOT on same circuit. Maybe lighter is broken and blowing fuse.

Tire compressor probably draws too much current for the socket. Are you sure it is a cigarette lighter socket? Some sockets are just to provide accessories 12v. Did a cigarette lighter come with this socket? True cigarette lighter sockets are generally fused at 25 or 30 Amps

Two very likely problems. Most likely, cigarette lighter element is "dead". Try one out of another car, since almost every one is the same. Second option is the ground wire, which would complete the circuit to make the lighter work. You need to ground the socket shell, and see if that fixes the problem.

CHECK YOUR CIGARETTE LIGHTER FOR FOREIGN OBJECTS, (COINS, PAPERCLIPS) MOST GMC OF THAT YEAR HAVE LIGHTERS THAT SHORT OUT. ALSO TRY DISCONNECTING THEM. DOME LAMPS, CIGARETTE LIGHTERS, VANITY MIRRORS, STOP LAMPS ARE ON THE SAME CIRCUIT. HOPE THIS HELPS YOU.

sometimes they separate those because one is a higher amp circuit (power outlet) versus a cigarette lighter, so check your fuses

In earlier model vehicles, the cigarette lighter is on the same circuit as the dash lights/ radio/ interior lights. Maybe it's not labeled as cigarette lighter, try other fuses. also, there should be a fuse panel both inside dash and under the hood. Also, sometimes there can be an in-line fuse right behind the cigarette lighter.

I'll give you a list of possibilities:

Fuse (but why did it blow)
short in circuit
cigarette lighter recepter is worn , shorted or dirty.
open in the circuit.

Check them out with a voltmeter.

Unplug cigarette lighter, check circuit, unplug each door individualy at first, Don't forget the back doors, check circuit. Usualy the door wiring is damaged but there may be more then two cigarette lightes depending on the model.

On some vehicles the cigarette lighter fuse is attached to the cigarette lighter assembly itself. Check if you can gently prise the cigarette lighter assembly out of its location in the dashboard, or remove any panel that may allow access to the rear of the cigarette lighter and look for the fuse (it may be an in-line one in the power lead to the cigarette lighter or it may be physically attached to the cigarette lighter itself). Failing that, the fusebox is normally under the dashboard on the driver side, but some fuseboxes can be found under the dashboard on the passenger side. There should be a diagram under the fusebox cover that shows what circuits each fuse protects. If a fuse has blown ensure that another of the same type and value is used to replace it.