I too suspect a bad ground somewhere. Have actually seen it on a car.
The fan is thermostatic it runs ONLY if the box is too hot. So it is not diagnostic.
To test you really need a voltmeter. Screwdriver Some protective covers (Wire nuts???) and a 12 volt light bulb with pigtail socket (most hardwares and all auto stores will have 12 volt 100 watt.
How to test
Remove all the 12 volt wires from teh converter Protect the exposed wire and make sure you know where they go (Color code or mark with tape)
In one pair of terminals lightly CLAMP the meter leads (WHen I say Pair I mean on the converter I mean one on the left and one on the right. Numbering them 1-2-3-4 I'd go with 2 and 3 or 1 and 4)
In the othe pair put the leads from the tunnel light socket Do not screw bulb in.
Plug in note voltage
Screw in bulb note voltage
Unplug and let bulb cool then remove
Post voltages to forum and let the experts rule.