Checked the fuse?

There's one fuse per coil. You'll need to check the manual or fuse labels to see what fuse goes to what coil). Though if you can find any blown fuses at all they'll need replacing!

System 3 uses a relay to control the flippers, no transistor involved.

The relay usually doesn't need replacing. At worst it might need a light filing or adjustment to the contacts, but that's rare, probably not the issue.

There definitely should be a big table of fuses somewhere in there. The bigger issue will be locating the fuse in the machine once you know which number it is

Run a wire between the outer two lugs/sides of that switch stack and see if the flipper starts working.

Switch test just shows what switches are closed. If there's a ball on the switch it'll register as closed

Shooter inconsistency is usually just play in the mech. Does it seem to have much wiggle side to side or anything? Is the ball resting against it well?

I'm not sure which style mech it is, but some have plastic bushings that can wear. Can't hurt to replace the sleeve on the coil either

There's a coil on the bottom side that moves the kickers. Inside the coil is a little plastic tube, the sleeve. They get dirty over time which causes sluggish and unreliable motion, so whenever you're having a mechanical problem with a mechanism the first thing to do is disassemble it and replace the sleeve with a new clean one.

Does the shooter rod brush the kicker at all if you rotate it?

See if the shooter strength depends on what way the rod is moved? It could just be brushing the rod and losing momentum.

Just order yourself a full rebuild kit. If the flippers are old enough that they're breaking like that, then both definitely need it