Pump should definately run for 2 seconds as soon as you switch the ignition on.
Relay is the first thing to go for. It should just pull out, however they can be stiff. On the Mk1 Golf's the fuse/relay box can be prone to water damage.........hope its not that.
Once the relay is out, I would bypass the relay, put it in test mode and carry out the following that I have just cut from the workshop manual:-
"Unless the fuel pump relay receives an rpm signal from the ignition system indicating that the engine is running, the fuel pump will operate for only a few seconds when the ignition is on. To power the fuel pump for testing without the engine running, the relay must be bypassed.
To bypass the fuel pump relay, remove it and substitute a remote switch, such as Volkswagen special tool no. US 4480/3 (order no. TU4 480 003 25 ZEL), or a jumper wire between two sockets on the fuse/relay panel. The correct sockets are the two largest ones located perpendicular to each other and corresponding to relay terminals 30 (battery voltage) and 87 (output to fuel pumps)."
" NOTE-
A home-made jumper wire should be at least 1.5 mm (16 ga.) wire and, for safety, should include an in-line fuse holder with a 20 amp fuse. To avoid damaging the relay sockets with frequent connections, the jumper wire should also include a toggle switch for switching on and off."
With the ignition off and the fuel pump relay removed, use the jumper (toggle switch off) to bridge the sockets in the fuse/relay panel. Turn on the toggle switch to operate the fuel pump. If the fuel pump does not run except when the jumper is connected, the relay or relay wiring is faulty. If the pump does not run with the jumper in place of the relay, the fault could be in the fuel pump or the electrical wiring to the fuel pump.
Good luck.
