Sounds like someone had converted the socket for the dual filament bulb. I did that for turn signals on my front parking lights. But it's not necessary for tail light, as the turn signal uses the individual (left and right) stop light bulbs. If you have 3 wires going into the taillight, that's likely what happened.

You might be able to use an LED 1157 (dual filament) bulb in place of the incandescent, which would generate less heat. They may or may not be smaller, though.

Kevin
1951 Chevy 3100 work truck
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1929 Ford pickup restored from the ground up. | 1929 Ford Special Coupe (First car)
Busting rust since the mid-60's
If you're smart enough to take it apart, you darn well better be smart enough to put it back together.