If my tail light was "pulsing" in time with the engine, I'd figure I had a loose wire.

 

Do you have a load equalizer installed as your LED turn signals will not operate properly without it.
Pulsating lights is an indication that you don't have a load equalizer.
LED tail light does not require a load equalizer just turn signals require a load equalizer

 

Sorry guys, televisions cycle at sixty cycles a second, if you record a TV the cycle will be off that is what causes the funny waves.
In order to get this affect you need something that is cycling and catch it while off.
Video cycles at a much higher rate plus LEDs are DC so they do not cycle period.
If you see them flashing it is because they have a flashing module.

 

Maybe set to one of the parade mode settings???

 

Or a short

 

A short would not cause this, a short would blow a fuse. An intermintant open circut could cause this but I doubt it.