Indeed, it had 4 contacts. I just want to make sure to get something that will have a long enough bushing that the top of the switch clears the escutcheon and neither mouser or digikey have anything that long. Dave Dintenfass suggested reaching out to Eaton (who now owns Arrow-Hart). I sent them an email but seeing that they're a multi billion dollar company with a vast and complicated website, I'm not holding my breath on a response. Fingers crossed though. I also emailed Carling as Ampex used switches from them as well.
He also sent me a ebay listing that's close, but there's a ball at the end of the switch that would prevent it from getting through the escutcheon.