1. Your '86 doesn't have one (it came with LH 2.4 on the '89 240s)
2. Even on LH 2.4 the Power Stage has no influence on the pump relay.

The following sequence list may help you to some degree. Note step 3-b:

Start-Run Sequence LH 2.2 Version

1) During starter cranking, the distributor Hall sensor sends timing pulses to Ignition Control Unit (ICU)

2-a) The ICU uses these Hall Sensor pulses to trigger the Ignition Coil (– terminal) to initiate timed sparks 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 Fuel pumping).

3-a) The Fuel Injection (System) relay (previously energized at Key On) powers the AMM and ECU. The System relay lives with the Fuel (pump) relay in the same white plastic case. The LH 2.2 "pump" relay also powers the Injectors, IAC motor/valve, and the O2 sensor heater.

3-b) When ICU pulses (2-b) are received by the FI ECU, it "energizes" the Fuel (pump) relay by grounding the relay coil (– side) to run the pumps.
EDIT:[Can be checked for at the relay, using simple 12volt Test Light probe.]

When all these things work, the engine runs until the Ignition is switched off, which in turn shuts down the FI system.

Determining if there is spark at the plugs (2a) — and whether or not the plugs are getting gas (3b) — are good no-start "starting" points.

--
Bruce Young, '93 940-NA (current), 240s (one V8), 140s, 122s, since '63.