There is a situation where flashers and flippers get mixed up and I thought it was a shorted winding on a flipper coil that does it. I fixed a big guns with a similar issue but it was a long time ago and I can't remember exactly what it was, but I don't think it was much more than a shorted coil and i had to patch a vaporized trace because of over fusing.

Trying to remember better ... I think flipper a coil plunger broke and button got mashed until the coil overheated and shorted. Then the fuse was like 20a and a trace acted like a fuse..... but Yeah i think it was on the interconnect board I repaired a burnt trace... Pushing the flipper button was still making flashers turn on. As that was the call I got was "push flipper button no flip but light comes on". Sounds at least similar to the OP's issue.

The Dr Dude magnet is on the 50v supply like the flippers would be but it has that tip36c high current driver. I'd have to peak again the circuit to try and wrap my brain around it but maybe a shorted diode on the high current driver?