This rubber pad is glued on the upper door hinge to act as a buffer against the dome light switch when the door closes. You may not have noticed this buffer; it is often painted over by previous owners.
This same light is used in the cargo area as well as between the visors. easily snapped in please check the light bulb and also the door switches when troubleshooting. remember there are two ground wires on one side of the light and the power lead on the other side.