I looked at PBR. I would think a lot if that would be replaceable but they exclude those EOS switches. Never seem those before and I have three mid 60s Williams games.

Why did they do that?

I don't think you are going to get a good answer to that, because I don't think there is one. I think they tried to get cute with the engineering, but it was just a bad design. The adjustment has to be just right for it to work properly, but here is how to make it work perfectly. Put a jumper wire across the NO switch (that is the low power leg) or bend the solder tabs together and solder them closed and forget about it. Adjust the NC switch (high power) as normal so that it breaks open near the end of stroke. That's it. When you first activate the flipper, current will flow through the path of least resistance (high power leg) until it breaks open, then it will flow through the permanently closed jumpered leg to hold the flipper up.

I'd just find what coil is used by the next game after this which doesn't use the MB switches. Install two of them and two normal NC EOS switches. Rebuild the rest of the mech as normal

I don't think I've ever played a Williams Big Chief before.

It reminds me a little bit of the Right EOS switch assembly on my Firepower flipper, where of course, one of the switches actuates the lane change feature.

Does this machine possibly use the EOS switch to change the state of something else on the playfield?

No, but that's the same thought Steve Young at PBR had when I talked to him about it years ago. It takes about 30 seconds to put a jumper across the NO switch and you now have a regular E.O.S. switch just like any other EM, and you can convert it back to stock if you ever wanted to in 30 seconds by removing the jumper.

Where do the wires on the second switch go? Can't tell from the pictures.

Compare the more common normally closed EOS switches in Alpine Club (above) with the make/break EOS switches on Big Chief (below).
Williams Flipper EOS switches (resized).jpg
In both cases the right half of the coil is the high powered kicking coil that is always active when the flipper button is closed and the left half of the coil is the low power holding coil that gets added into the circuit by the EOS switch at the end of the flipper swing. Jumpering across the normally open part of the switch in the lower example as sudsy7 suggests would make the circuits the same although the flipper coils are different.

/Mark

Of course you can do that if you want to do the extra work, but if you just bend the solder tab of the the NO switch to the common wire and put a dab of solder on it, it is essentially the same thing - just much easier. You will not get any more performance doing it the other way (unless of course you change to higher power coil).

So why not just tie the two wires to the n/o side together and use a regular EOS switch for the n/c wires?

That's exactly what he intends to do from his post #12.