I've never tried it but the -ve wire that is controlled by the ECU would switch very quickly so I don't know if you would see it with a digital meter, possibly with an analog (needle) type.
You say you have 12vdc on the brown while cranking, so the ign switch is not the problem
Even with a bad ballast resistor it would fire at least until you released the key - then it would die. So I would cross out the ballast resistor and switch out the ECU.