When you mention pinching the contacts together with success, I've had more that once, the contact itself building carbon between the rivet itself and the leaf hole. A solder joint on the back end cures that to bond the two together.

Since the target relay AND the outhole relay are tied together per the schematic -both trigger the score motor exactly the same.
Weird issue.

Here's a trick. Room lights off or dim. Go through the sequence with the play field up. Look for the biggest arc. Continuity shows one thing, current draw shows another.