...I felt like I should respond to this:

"I assume that the crank position sensor is realyl for starting up and is not relevent after the engine is running, is this a correct statement?"

No. The CPS is basic to ignition timing for both starting and running. You'll see it as the first step in the following start-run list of events, but it's pulses are required for running as well:

Start-Run Sequence LH2.4 or Regina FI

1) During starter cranking, the Crank Position Sensor sends timing pulses to Ignition Control Unit (ICU = EZK or REX)

2-a) The ICU uses these CPS pulses to trigger the Power Stage (aka Ignition Amplifier), which initiates spark from the coil.

2-b) At the same time, The ICU also propagates the pulses to the FI ECU, to allow FI operation (no ICU pulses means no FI operation).

3-a) The Fuel Injection (System)* relay (previously energized at Key On) powers the AMM, IAC, ECU, Injectors, and Fuel (pump) relay coil + side.
* The System relay is in the white case with the Fuel relay.

3-b) When ICU pulses are received by the FI ECU, it "energizes" the Fuel relay by grounding the relay coil (– side) to run the fuel pumps.

When all these things work, the engine runs until the Ignition is switched off, which in turn shuts down the FI system.
--
Bruce Young, '93 940-NA (current), 240s (one V8), 140s, 122s, since '63.