I suspect that the ball popper, drop target and shooter switches also don't work. Check that the green-violet wire is making a good connection at J207-7. If so, follow that wire back and make sure it isn't broken or shorted somewhere. If you have a manual, you can see that all of these switches are in the same column on the switch matrix and they are all grounded by that green-violet wire.

+1 You most likely have a broken wire somewhere in the chain leading to those switches.

You will have to look at the switch matrix diagram in the manual. If you check two ends of each wire (like on the non working target and another switch in the same row or column) that will work with continuity check. The diode will not effect that.

Your probe will fit. Otherwise, you will see a bit of metal for each pin on the side of the connector that you can touch with your probe. If you stick your probe in to the connector, do it gently so that you don't bend the blades that are making contact with the wire.

In OP checking the continuity between switches, would the switches have to be closed to keep continuity?

Congrats on finding and fixing the problem!