the green/ red we know from other threads is a pulsed signal from the coil

brown white is the negative to the cold start injector, the +12v for this injector comes from the starter motor solenoid wire as it only fires when the engine is cranking.
brown/yellow would be a input from the thermal time switch, this switch gives its output
for a maimum of 5 seconds only when the sensor is below 35degrees(should have this stamped on it)
red/black is a positive output that switches the solenoid on for the over run valve, this should only operate when revs are above 1500rpm ad the throttle is closed, its designed to allow the metering head to shut when decelerating, modern ecus just shut off the fuel to the injectors so this is a crude version of that

so from the wiring i assume that it operates the cold start injector and the overrun valve, from youre previous threads it does sound like the cold start valve is probably working as it starts briefly, the overrun valve should be closed and this can be checked just by blowing through one of the big outlets on it, if you cant blow through it then its closed,

the cold start injector can also be easily tested by placing it in a plastic cup and cranking the engine and see if fuel comes out,

i have no idea how else you could test this unit, apologies if ive gone over stuff that youve already checked or stated the obvious.