A couple of points on your 1990 740, the fuel pump relay passes current to fuse #11 for BOTH fuel pumps - on later 940s it feeds fuses #11 & #13, one for the main fuel pump and the other for the lift (in-tank) pump and Lambda sensor heater. It's worth checking that fuse #13 is intact on yours, just in case yours is a leter 740 with a 940 style electrical system.
Clicking from the relay means it is operating mechanically on the control signal, it doesn't necessarily follow the contacts are passing current to the pumps - hence my test as described above to see if power is reaching the in-tank pump.
Information about the early LH2.4 (as yours is) is a bit hazy about whether it reprimes after the ignition is switched off and then back on again, as Rob says on later models there is a time delay (10 minutes i think) before it primes on first turning the key to position 2 but either way, if the starter runs the engine, it will trigger the pump to run for a second or two after it is released from position 3 - this is normal across the 7/9xx range as long as it's electronic injection.
Run through those tests i outlined and see what you've got. If the tests don't give the results i suggest then let us know. As for the pdf Rob linked to, there are many differences there to how yours is set up, for a start the author claims he has LH2.2 but has a Lambda sensor.
Not for UK models at least, that would be an LH2.4 which yours is.