These are cheaply made chicom lights and anything could be wrong with them.

If the vehicle battery is good and the esc is good and if you plug one light into a spare receiver port and it does not light then the light is probably broken.
Plugging it directly into a 4.8 or 6 volt battery will prove if the light is good or bad.

The signal wire is probably only used to change the flashing sequence .........when they are working correctly.