If the glove box light works with the key on, and the 'Power Outlet' does not, then you have a broken wire or a faulty/dirty 'Power Outlet' : they are common to the same fuse / power source.

( I know this because I tapped the power there for my Garmin )

I wired in a female 'Power Outlet' and connect to it behind the removable dash panel that has the air bag key .