Ford Focus Reverse Light?

This is driving me crazy so hope someone can give me a pointer to what might be causing the problem.

Basically, reverse light isn't working.

Things I've tried:

1) Swapping Reverse Switch (at garage, who said it made no difference)

2) Checking reverse switch function (at boot connector, with car in gear and out of gear), checked bulb-holder, checked reverse connector (in boot) All with multimeter. All report voltage (@11v).

3) Took the bulb holder (and bulb) and swapped with Fog Light's bulb connector (moving from Reverse connector TO Fog Light connector) so bulb holder and bulb are ok.

4) Put an LED across the reverse light connector and it lights.

5) Attempted to put wires into the connector and connect the bulb (ie remove the bulb connector out of the equation) - and the bulb didn't light up! (but an LED did…)

6) Spraying connectors with Electrical Contact Cleaner (made no difference) - they didn't appear corroded anyway.

7) oh and fuse checked too (it's on the same circuit as wing mirrors and they work)

So to confirm.

1) I know the bulb works
2) I know the holder works
3) I know the connector is putting out 11+ volts
4) The ground works (hence successful LED test)

Could the amps/watts be insufficient to light the bulb, even though the Volts read 11V?

3) I know the connector is putting out 11+ volts Well the bulb needs 12V so you have a power drain somewhere!

Check the ground connection - an LED only draws a few milliamps, but the normal 21W reverse light bulb draws nearly 2 amps. The ground connection may only be passing enough current for the LED…

Led's don't draw enough current for an accurate test.
make yourself up a tester using wire/s alligator clips a bulb holder and a 21W indicator bulb.
That'll draw around 1.5 amps, depending on battery V.
How to use it?
forget about switches and fuses.
one end of the tester goes on bat+, that makes the other end live, touching it to ground and it will light, and light bright!
now connect the lamp to the reverse light switch pos/bat+, ground the other test lead,
it should light the lamp, if not there's a reverse light supply fault,
and it doesn't matter a **** if a multi meter says there's battery voltage at the reverse light plug!
ONE strand of wire will carry 12V but it won't power anything!
Or you can inject 12V into the wire that runs back to the lamp and then run a temporary earth.
Led testers are misleading.
the circuits your working on run at least 1.5 amperes.