Maybe a faulty PIA or Faulty Electrolytic Cap on the driver board or power supply or mpu.
Or a faulty diode on the flipper relay.

I have a similar fault on my BK2000 but it's intermittent and I haven't rebuilt any of the boards yet. (yes I know It's a different system)

do all the lamps pulse on start up also?

Maybe when the transistor died it damaged the I.C.or PIA that drives it which is sending funky signals to the data lines.

if you have a spare driver board or one from another machine try swapping it to confirm if the fault is on the driver board or else where.