Quoted from frunch:

Do all the other playfield switches work?
Have you tried cleaning/adjusting the switch? You can use a business card, clean piece of paper or $100 bill to slide between the switch contacts.
Verify the wiring is tightly attached to the solder lugs as well as the diode.
Sounds like the coil is ok, so I'd focus on the switch for now.

Quoted from frunch:

Have you tested the switch for continuity with a meter? Might just be worn out contacts (especially if they ever got filed, which will damage the gold plating on the switch). I know a lot of Williams switch stacks were assembled improperly, so the stack has one contact facing the back side of the other contact...if that's the case, you may just want to replace the switch anyway for long-term reliability.

Quoted from slochar:

Does it register in switch test? It's definitely not the original switch, williams didn't use switch stacks like that with all the holes... those are gottliebs'. Ignore that the game ejects them at the end of the game, that routine is 'dumb' - it just ejects all 3 holes regardless of their contents.
It's on the same row as the top center target so it's possible that the row chain is bad. Check the other switches on that row, follow the wiring around the playfield and tug on each set of wires (there should be 2 going to each switch except for the last one in the chain which is not necessarily the last switch logically in the row)
The lug without a wire on it in your picture if that's the blade, it might have been bent to touch the lug with the diode as that's where the diode would go. Maybe whoever rebuilt the switch stack just bent the lugs together instead of soldering a short jumper.

Quoted from slochar:

You should get all closed switches registering. With the 3 balls in the trough the switch test should cycle through 51, 57, and 58.

If there's a loose wire tugging lightly on it will cause it to come off or you would be able to tell that the wire isn't making good contact. To fix that you solder the wire back onto the lug. There will be 2 lugs on each switch that have wires going to them - each lug will have 2 wires except for the ones that are at the end of the line, they only have one. The rows should all be white wires with varying colors of stripes (your eject hole is on row 5, white with a green stripe).
For that era machine (for my firepower specifically) I rebuild every single switch stack with new parts - like Frunch said, some were filed or put together wrong at the factory. 40 years has taken its toll. I replaced all the switches in my firepower for exactly this reason.
The early production/proto wiring isn't as uncommon as you'd think. Lots of the wire harnesses came out of the factory with the wiring in place. What's odder is if you have the playfield with the cutout for the 10 pt standup switch behind the 1-6 targets.
I've played a retrofit FP with the drops installed, it's not as "in your face" as good standups that rocket the ball back at you (and down the outlanes) which I find challenging. I was originally going to retrofit mine since I have the parts, but decided not to. (it might be interesting to see if a retrofit drop bank PLUS standups ala Bally would shoehorn in there, but I don't think there's room.... I'd have to come up with another type of standup for it to fit. That way, your first lock would be 'easy' to light with the drops, but the subsequent ones would be difficult.)