well either 30 or 87
should be loose (I thought 87 but cannot remember exactly)
but you said it's 30 and that might be it.
(I thought 30 is the one 90° apart and the one you're holding is 87...anyways)
In fact it must not be connected at all.
You see the electro magnet in IMAG0622 and see it protruding the pcb in the following pictures.
Once it's engaged it will pull the loose contact to it's copper plate and make it connect to 87 (closing the circuit and running the pump)

but there should be a spring IIRC ...
I'm sorry it's too long ago to remeber how mine looked on the inside
But again either 30 or 87
must not be connected in non engaged state.
That's a UH2 relais isn't it?
let me see if I can find any internal schematics...
Now for the previous post..
The loose connector you found (brown,darkgrey) looks to be T2c in the wiring schematics (left blinker or T2g right

) I have no idea why it's that close to the engine.
It's hard to tell where the connectors are located relative to the engine on your pictures,
and I don't want to make wild guesses..
it's alread messed up, and I don't want to make things worse
Let's bypass a 'broken relais' for a real quick test:
Find the slots on the relais socket for ppin 30 and 87;
turn the ignition off, and bridge the two connectors
turn the ignition back on and check if the fuel pump is running or not,
turn off again, remove the bridge and you know if it's the relais or not.
(not as precise, but much quicker until we find the connectors to check in the engine compartement

)
Do not leave the bridge in longer than absolutely necessary to know if your fuel pump is running.
(that's the post #126/127 thing!!)
Also, Now that you say it.. the drawing I posted above might not be very precise
(might be a different engine depicted maybe even a G60) but it was the only one at least close to help locating the connectors.
Anyways.. you can measure the exact same thing directly at the relais socket;
it's just the other end of the wires.
same numbers apply (2->ground, 4->ground , 4->6)
[
EDIT]
I just crosschecked.. the image was BS!!! indeed a G60 completely different harness

My fault, removed the image and stuff above...
test directly at the relais socket, that's the only way I can think of unfortunately.
And while you're at it, add 1->ground to the testing procedure
I think 4->ground is useless, since 6 is ground anyways and 4->ground and 4->6 should behave exactly the same way....
if not you'll know the groundwire 6 causes the failure ... so maybe not too uselesss
I'm sorry for the confusion I caused.. liquid cooled VW are not my specialty
'sid