The ignition system is totally separate to the ecu for these models. They work in exactly the same way as the blue motor ignition systems.
Try replacing the ignition module - this is the problem 99% of the time. Old corollas/pulsars etc use a bosch dizzy with the same module. I used to grab them from the wreckers cheap a few years back. Always good to keep a spare in the car.
The tachiometric relay takes signal from the ignition, starter and the coil. So without ignition pulse it’ll only prime the fuel pump shortly then stop, will power the pump when cranking and that’s it. Should hear the relay click on and off when it ‘primes’ when ignition is turned to the on position.