I installed one light on the trunk, and had the same issue.
How do you know if its the led you bought or some ground / cable in your car?
Simple, if all the leds of the led strip goes off, then there is a problem with your car connection.
If only 1 led bulb from the led strip goes off, then you have a bad led strip.
For the license plate led replacement you should have around a 5 led strip system.
Honestly , in my 12 year as a honda enthusiast I've never seen a electrical interior light system fail ...