It might be helpful for you to download
BMW's LE Jetronic training manual from our site to understand how the electronics work.
First off, at the fuel injection relay there are two 87 outputs—one line from 87 and another from 87a on a five pin relay or two lines from 87 on a 4-pin relay are sometimes found. One line goes to the throttle switch and one goes into Fuse 6 to power the fuel pump and to activate the temperature sensing unit. Two lines come from Fuse 6 output—one goes to the pump; the other goes to the temperature sensing unit. If you test the wrong combination of wires at the relay and Fuse 6, or at the output side of Fuse 6 and the pump connector you will, of course, not get continuity. There is also a possibility of a broken wire in the circuit wiring or a defective relay.
Power to run the fuel pump in a K100 occurs when the ignition control unit (ICU) receives the starting signal. The signal is delivered when the ignition switch is turned to On, the starter button is pushed, and the engine is cranking. 12V should then delivered to the fuel pump connector to start the pump.
Here are two schematics downloadable from forum member
frankenduck's comprehensive Brick information site. They can be enlarged until the relay terminal numbers—on the schematic that has them—can be read.
1 2 There's at least even money on my having a correct understanding of what's happening on your side of things, or things in general.