if the fuel pump runs and the tach shows signs of movement, then the ECU is
definitely receiving power on ignition switch on.
Looking at the DME relay ........pins 85 & 86 energise the first relay coil when the ignition is switched and supply power to the ECU , injectors and various sensors via the ECU, so the first checks should be on the DME relay base with the DME relay removed and ignition off.
1. Check that pin 85 ( pin 1) is permanently connected to ground using a multimeter switched to continuity(.If it whistles its good)

if it doesn't then check and clean the ground points (brown wires)
2. Check pin 86 (pin 3) has no current with ignition off
3. Switch ignition on and check pin 86 now has 12v+ (battery voltage)
4 Confirm that terminal 30 (pin 2) has 12v battery voltage with ignition off and with ignition on.
If this all checks out then the issue lies with the second relay coil not being energised by the ECU .
Reasons could be many but it is
very unlikely to be the ECU at fault .
The ECU will only function when all the various sensors send a satisfactory signal to it.
First and most critical is the engine speed sensor. If you are seeing a tach bounce then the sensor must be receiving power from the ECU
If the tach needle doesn't bounce when cranking the engine then either the engine is cranking too slowly (needs to be 200rpm min ) or the sensor must be too far away from the flywheel starter ring or there is a fault with the sensor , the wiring or the connectors between the sensor and the ECU
The speed sensor should be your next check before looking at the ECU ........follow a logical sequence based on testing and don't change or adjust things at random