3R Headlight fault

[Nailgundan]

Last night my offside low beam went out on my 3R on a 2 min trip.
So today I....
Checked the fuse, was ok but I swapped it with the near side one just to be sure.
Checked the bulb, it was blown, replaced it with another one. No joy.
Checked the new bulb on the high beam circuit and the new bulb is fine. Connected the highbeam bulb to the low beam circuit just to be sure, no joy.
So at this point I have two bulbs that I'm sure work but not on the low beam circuit.
Out with the multi meter, 11v on the low beam circuit, 14v with the engine running?
Swapped the relay with the main beam one at this point I'm grasping at straws, still no joy.
Gave the inside of the connectors a rub with a little bit of wet n dry, no joy
Dragged my father out into the cold for a sense check.

Put the kettle on and started typing.
Ideas or sympathy most welcome.
Is it possible or likely I can have correct voltage but insufficient current to light the bulb?

[StreetDragster]

It sounds like you have two blown bulbs.

If you put 12v from a jumper pack or something across the bulb, does it light?

[Nailgundan]

The original was blown, the new bulb and the one stolen from the high beam both work.

[kenloen]

sounds like you've got a low beam connectivity problem. when you measured the 11v and 14v where did you earth meter (chassis) ? .. its probably either an earth wire or the bulb socket itself.

[Nailgundan]

I connected the meter to the two spade connectors that connect to the bulb, so I guess I could continuity check the earth wire to the chassis.
But to add insult to my confusion, I had given up for the night and decided to take the spare car, so I close the clam, back the noble out the way and as I park up the head light comes on!
So I have a poke around, take the bulb in and out and it's stable, I can't reproduce the fault. As I'm not a believer in magic I'm guessing this is going to come back and bite me at some point but I still don't get quite how there is the right voltage but not enough current to even get a flicker/dim glowout of the bulb?

[PaulM12]

Similar response to another post, but check the contacts in the fusebox / on the relays. Quite commonly corrode and cause poor connections.