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That looks like an aftermarket EL gauge cluster overlay... If so, that little black plug goes to the inverter box, wherever it was installed. Probably under dash or behind the cluster?
Bingo. I recognized that plug as the standard plug most single gauges and overlays use to plug into the inverters they come with. A cheap solution to pass inspection would be to connect a length of wire to each pin in that connector and run them to a nine volt battery. That should power them long enough to pass inspection. Doesn't have to be able to turn off, just has to be on.
On a side note if you have the vehicle that far apart I bet if you pull the cluster there are no bulbs in it for the backlight at all, install some and give it a try, "*MIGHT*" be bright enough to pass inspection that way.