Basic electrical skills...

Wonder if a cleverer head than mine can help with a simple electrical problem;

My rear fog light doesn't work. The switch works, in so far as there is about 10 volts arriving at the bayonet fitting in the rear cluster WITHOUT the bulb fitted. The earth I believe is good and clean, and the tail and brake light run off the same earth and work fine.
The jumper wire across the rear clusters to make the fog light work on the right for the UK market is ok too, although my testing thus far is just to the left hand cluster terminal, as this precludes one more problem area.

My problem is that as soon as I fit a bulb the voltage disappears and, of course, the bulb does not light. I tried a 1.2w dash bulb across the bayonet terminals but even this did not illuminate and the voltage still dropped to zero.

Am I right to assume that there is a very weak link in the live side of the circuit, so that with an open circuit there is voltage, but with any load whatsoever completing the circuit, that weak link (like a single strand of wire or very poor connection), draws the current instead?

Should I check the resistance of the live (switched off obviously) wire from the cluster? And if so, to where?

Any help with getting my head round what I'm looking for would be greatly appreciated!

Cheers

Might sound a daft question ? Do you mean you have one bulb fitted ? Drivers side with as you say fog light strap fitted ? No bulb in pass side ? You should have one bulb , drivers only .

Fuze is [gti model] above relay 5 and you should check voltage there , 12v ? yes , wiring to rear faulty . No 12v ? Switch faulty or supply burned out .

Live comes from fuze box and unless thats flooded [wet] should be present at fuze  mentioned above .

Cheers………….