I went through something similar to this glove box problem when I bought my 1995 S420. My problem stemed from the wire bulb lead wire not being connected to the main wiring loom. Check for 12v at the socket. Access is fairly simple, I did it in the parking lot of a local hardware store with limited tools. Remove the glove box and trace the wiring. A service tech may have just forgotten to reconnect it like in my case.

Regarding the lighter. I repaired my E320's lead wire to solve the same type of problem. Over the years the constant opening and closing of the ashtray fatiqued the wire at the lighter connector. I just re-terminated the existing connector to the wire.

Good luck.

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1995 E320 -171k-km
1995 S420 -333k-km