I had an issue like that with some Christmas leds once. Wouldn't work unless I touched the plug... for some reason when I put a dime on the plug it worked fine again lol. I was worried that there was a short somewhere in the plug so just replaced the plug.
If your lights are wired through a power supply the power cord should simply be hooked up with a terminal screw. Easy to swap out...
Another question would be where do you touch for it to start again? The heatsink? Drivers? A wire?
You would even need a multimeter to check for a short. A simple buzzer would do the trick. Just make sure you unplug it before buzzing
What kit is it? Rapidled or aquastyle,