To start with, your drop target reset solenoid shouldn't be that weak. Try putting a new sleeve in, or taking a look to make sure everything's good on the mech.

Your motors get voltage all the time. They only move when that voltage can get to ground. My top-of-the-head guess is that you've got a chip starting to fail on your driver board, and it's leaking tiny pulses to an adjoining data line. It may be leaking tiny pulses to all data lines, but they're small enough you don't notice them on the solenoids. Another possibility is that something is grounding out the returns when the machine shakes. In any case, it's not voltage related, as you can see what happens when the door is open and the 50v is disabled.

Weird. I've had two JD's, and I don't remember either of them doing that. Then again, I see a whole lot of pinballs, so I may have forgotten.

Let's see. It would be...put your logic tester on pin 15 of U5. See if it flashes when you fire the drop target solenoid. If it does, something's leaking where it shouldn't be. If not, check your grounds. Make sure the driver board is screwed in well. Check to make sure the legs of Q64 are soldered well, and have no cracks.

Pulling the power for the motors doesn't really prove anything. Still, next I'd try taking a look at the diodes and the inductors on your motor boards.

j118 is indeed the power. You pulled the power. Ignore this post. "drive" and "voltage" are reversed in the solenoid chart for those. It can't be getting voltage from a drive transistor...I don't think

What I would personally do at this point is cut the violet/blue and violet/yellow wires, and see if they still move. But don't do this if you don't think you can patch it back together.

...pretty much wherever in the head. It doesn't matter. Some place where the wire's not tied up in a harness so you can access it. I'm almost positive they won't move, but one test is worth 1000 opinions, and all that. The idea is to isolate the motor's ground wires from the other ground wires in the game. So a break anywhere in either of them will prevent them from moving, unless there's a short to another wire.

Edit: In the head. Cut the wire in the head. I figured it was clear, but realized I never said it.

Well, jumping around those wires pretty much proves that whatever it is, it's in that board. So if you decide to buy one, it will indeed fix your problem. Also, what happens with those drop targets if, say, only one is down and it tries to reset? You might have a bad switch there.