Check the DC voltage at the point where you connected the LEDs to the car's electrical system.
If you have two wires, test between them and see what voltage you are getting.
If you only have one wire, test between that and the a piece of bare metal on the frame.
It just occurred to me that you just might be having a poor ground so make sure that you have a good clean connection on the ground side of the wiring. Normally this where one of the wire is screwed into the body. frequently rust at this point will impact the ground connection
this may also be the problem with your old Dull lamps.. I gave my Son a pair of stop tail lamp LED bulbs as they weren't bright enough for Me... but there are new ones out Now with LEDs facing outwards too.. but I did add grounding wires to his tail lamps.. when i wired them up.. LEDs are very low voltage items, if 12v is put thru them they will burn out instantly... otherwise they will last just about forever.. cheers LEE
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