Paul, thank you for the help, I have managed to get the glove box off, and can see why the light doesn’t work.
I am going to see if I can glue the left hand side plastic fixing, but I don’t think it will hold.
I took the carpet out which felt wet to the touch, damp even. I have checked the under floor compartment and that’s dry.
So I’m thinking just condensation.
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I'd also check the AC condensate drain. It's the rubber hose at the top-right of the picture, going through the bulkhead. The outlet gets mucky and the hose backs up with condensate that then drips from under the glove box. Pull the outlet out of the bulkhead, lift the flap at the end and clean it out with a pipe cleaner.
Admittedly it seems unlikely to be the cause given the time of year, but well worth doing while you're there.