First, swap the bulbs left-right. If the problem moves it's the bulb, regardless of what it looks like. If it isn't the bulb, you should be able to put the car in reverse with the key on but the engine not running. That will give you a safe opportunity to remove the right-hand bulb and test the contacts to see if you are getting 12 volts. If you do, there's something keeping the (apparently good) bulb from properly contacting the socket. If there's no voltage across the contacts, you may have an unplugged or damaged wire or connector. They shouldn't be difficult to trace inside the trunk.

Jeremy

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"Buster" in the '95

Our all-Diesel family
1996 E300D (W210) . .338,000 miles Wife's car
2005 E320 CDI . . 113,000 miles My car
Santa Rosa population 176,762 (2022)
Total. . . . . . . . . . . . 627,762
"Oh lord won't you buy me a Mercedes Benz."
-- Janis Joplin, October 1, 1970

The plastic base that the rear tail lights screw into are notorious for too much Heat, causing them to melt.

You need to buy a new base and wire it in.

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Paul S.

2001 E430, Bourdeaux Red, Oyster interior.
79,200 miles.

1973 280SE 4.5, 170,000 miles. 568 Signal Red, Black MB Tex. "The Red Baron".