(Ford) KE-Jetronic always came with two ECUs. Ford ESC-II for the ignition control and the black Bosch Jetronic Module for the KE-Jetronic control.
Both work independent, the only connection is an ignition signal from the ESC-II to the Jetronic module when the engine is running. According to the wiring diagram the hall signal from the distributor (green/yellow; PIN 20 ESC-II) is directly connected to the Jetronic module (green/red; PIN 20 ESC-II -> PIN 25 Jetronic).
The fuel pump relay is connected to the green cable (PIN 1, ESC-II) to the ignition coil; green/red. Wiring might be an issue or the ESC-module. You could try another ESC-module or throw it out and use an aftermarket, mappable ECU for the ignition control.
P.S.: ignition feed fuel pump relay is for safety reasons. When the engine cuts out after an accident, the fuel pump will stop delivering fuel and therefore reducing the risk of a fire.
Your temperature gauge is for oil temperature. Water temperature usually is just up to 120°C, as more doesn't make sense. Most aftermarket sensors come with the same thread as the Ford sensors for the temp gauge in the dashboard. I'd get a (VDO or any other good aftermarket gauge) temperature gauge and a new sensor.