That first video tells a big story there. That fast strobing there is the power supply bouncing off the temperature cut off there. When you see it at that fast rate there, time to turn them off or they will be damaged. They are running very hot.... which also explains why the solder under the LED pads are re-flowing as well, as it takes 250-270C for that to occur.
What would cause it?
- Low voltage input.... over an extended period of time
- Current sinking through the bulbs due to something else on the circuit
Most likely culprit.... the current.
What else is wired up to, tapped off of, referencing from the reverse lamp and associated circuit?