Hello ...
as you have said, the noise comes from behind the co -pilot's gloveard, and if I'm not mistaken it is a relay that "went to a better life."
Try what he tells you efficiently with the switch, but I think it will be the relay, and surely the noise will continue when putting the contact.
The truth is that it is a breakdown too much expensive to solve (change the relay), for the result (utility) you are going to obtain. The simplest thing is, disassemble the glove compartment, disconnect the relay, take the cables, and re -mount the glove compartment, in my humble opinion.
All the best.