Defo earth problem, I do hope the RAC man removed ALL the bulbs when testing ?, as otherwise these wil find a natural earth path through the filaments, as they are all connected to earth!!
Best bet is to run a seperate earth wire to the earth ring on the lamp holder part from the lamp inner fixing screw, cures the earth problem permanently, just drill a 3-4mm hole in the earth track, roughen the area and solder a wire on, then to earth on the fixing screw.
I actually hard wire all my rear lights in as these are problematic on fords of this era anyway.
Can also do the fog/stop light mod at same time if wanted, costs about 10 pence and massively effective, mot passable and legal.
tabetha