Does anything else work in that socket?
Is the dropper a "plug in, socket out" type? If so, does anything else work plugged into it?
Just because the cable is rated at 11A does not mean that it will somehow pull 11A. If the dropper maxes out at 8A, that is all that is going to go through the cable, so it isn't going to act like a big fuse and incinerate your cab. Similarly, what the cable actually does carry depends on the load at the end, a big load will pull a lot, a few LEDs will pull very little. LEDs should be at the low end of current draw.
Assuming that there is 12 volts coming out of the dropper, and the lights don't, current is not flowing through the lights. Either no volts getting to the light unit, or the current is going elsewhere.
A broken wire stops the current. A bad connection counts as a broken wire.
A short will bypass the intended load, so the lights will stay out. This usually results in the fuse blowing, same eventual result as the broken wire.
LEDs are polarity sensitive, so must be connected the right way round. If not either a safety prevents both operation and damage, OR they die. Either way, they don't light up, but if there is a safety device in there, you get another try without buying again.