so any recommendations with where to go with this?
Connect a CGA monitor to the elevator controller.
The signals are clearly digital, since they go straight to a couple of TTL logic chips on the monitor's board. You keep going off on tangents trying to match up connectors, but that square 8 pin connector was never standardized. Just because a Tandy CM1 or some other monitor used it, doesn't mean another system using the connector used the same pinout. I've got monitors that use it for analog RGB, and I have some VTR equipment that uses it for composite video. Likewise, you mention this square connector, and BNC connectors, and the connector on the monitor's chassis - but I don't know where or in what order these connectors exist on your system. That 8 pin connector might be a dead match for the pinout of a CM1... it might not. No way to tell without looking. Follow the wires and see where they go. Since you were able to get some kind of video on the CM1, then it might be the same pinout. In which case, building an adapter cable to a CGA monitor is trivial.
When you got a picture on the CM1, were all the colors there? Was it recognisable to what you were expecting to get, just out of sync? If so, then it's more than likely the right pinout, and your above cable should work.
Since I have never seen this system, I don't know what the wiring looks like. But, to generalize, between the controller/computer and the monitor, there must be some kind of cable. In that cable, on whatever connector it uses, is going to be the three colors, sync signals, ground, and probably an intensity signal. You need to find these signals and connect them to a compatible monitor, which, I'm making an educated guess is probably CGA, based on the interface and the application.
Based on the photos you initially supplied, I tried to give you the pinouts back in the second page of the thread, but I also don't know where all the wires in the video interface cable go. You mention another connector that plugs in elsewhere - but don't say where that is or show a picture of it. That might be your intensity line (it'll go to the video amplifier circuit somehow).
-Ian