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Try looking in the fusebox
The owner's manual doesn't specifically mention the glove box light. But I would guess it is either #14 or #19 on the Interior Fuse Box.
The interior light fuse on the 2003 GMC is located under the rear seat on the driver's side in the back fuse box. The fuse is number four.
There should not be one for the interior light.
you can pull the fuse
CHECK BOTH THE INTERIOR FUSE AND THE COURTSY FUSE
The fuse that says "room".
i was told its the same fuse as the interior light
interior light fuse
In the fuse box.
Fuse 15
Interior light