On my coach all 12vdc is wired with 14 AWG wire.
The ground effect lights are part of 2x 15 Amp circuits. The Porch Light (Curb Side) and Scare Light Road side) circuits.
Typically an LED strip will draw about ½ Amp per foot but use the data supplied with your favorite flavor.
I doubt you would add enough LED strips to overtax 14AWG wire.
My extra $0.02 is to just replace the ground effect pucks not add to them.
Wiring Diagram
.
After re-reading your post it seems you may be thinking of tapping into the smaller gauge wire of the puck. Do not do this. Find the 14 AWG it is spliced into as Bryan said.