If your comfortable soldering moving the 25v wire is pretty straightforward. I acquired a f-14 a couple months ago and had to do a lot of the same troubleshooting.

Have you made sure the micro switch on the wireform leading to the kick out is registering. If that switch does not register it will not kick out properly. Same goes for the switch that the ball sits on.

Yep so the short sweet version. there will be a red wire attached to the pop bumper. there is purple and yellow on the diverter. you remove the purple yellow wires from the diverters (they are on a daisy chain so your essentially removing a section and then hooking the power back in at another 50V coil. Yagov is closest ). Then you run a wire from where the red wire is on the pop bumper over to where you removed the purple/yellow wires. I promise if you take some good pics me and grumpy can get ya sorted. This is what I did with mine. I went back to the fuse so everything looked close to stock but you can just add 1 wire from pop to diverter and accomplish same thing.

https://pinside.com/pinball/forum/topic/williams-f-14-tomcat-2/page/2#post-4867195

I need to look at the pictures harder. I saw it was mentioned then looked at the blown up picture and somehow thought it was the diverter coil my bad. So yes you are good on that aspect. I guess I’ll ask the question. What are your plans for the machine. Are you just trying to get it playable or are you looking into more of a restoration? If you wanting to restore it to good working order I would start by making sure all the fuses are the correct values. Then start pulling individual coils and rebuild them. Enough diodes (coils) for the entire machine would only be a few bucks. Also willing to bet a good majority of your coil sleeves need to be replaced. You do this all at once. One coil at a time. The first couple will take a little while but once you get the hang of it it is not that bad. I did all mine over the course of a week Couple hours a night getting roughly 4 done. If you just wanting to get it playable look at all the coils and make sure they have diodes like grumpy had mentioned. Once that’s sorted run the coil tests. Test a single coil and let it fire several times to see if fuse pops. The balls getting lost in the right lkickout start with switch tests. I had the same issue with balls being lost over their and it ended up being the switch at the top of wireform that leads to kickout.