Kip, sorry this won't help much, but I have noticed sometimes it takes someone to make the first reply to a post in order to get the discussion rolling...... So with that objective...
I am assuming you are talking about a "Contactor". Generally, a contactor is essentially a hefty relay dedicated to switching a big load, such as a motor. Since your machine is old, and relays and contactors are subject to age and load related failure because of their mechanical construction, maybe your contactor has gone intermittent. The contacts are most likely to fail. And if the contactor's contact ratings are not appropriately matched to the load, contact failure is more likely to occur. Even having a contactor with a rating way higher than the actual current being switched can result in contact failure, when a mechanism called "self wiping" will not work.
Someone with a volt meter, a schematic and basic electrical knowledge should be able to help diagnose if the contactor is bad or not,,,, assuming that it fails to work regularly.
As to your emergency stop button false triggers, I have had the same thing happen with my machine ever since I have had it. It is random, and I have changed grounding as directed by others, and thought the problem was gone, but then it pops up again randomly. That may be harder to figure out than the contactor..............
Good luck, hope someone who really knows these machines can chime in, Chuck
Chuck Keysor (circa 1956)
PRT Alpha 60" x 144" (circa 2004)
Columbo 5HP spindle
Aspire 9.0, Rhino 5