1 or 2 dedicated 120VAC circuits for my CNC?

Output
hm2_7i76e.0.7i76.0.0.output-01
is the second pin on the header, not the first
just to be sure

Yes I have it correct. It is the second pin.

Use a DVM to measure the voltage change on that pin, if you can.

Also, watch the output pin in halshow if it is changing state.

I checked the pins and both pins are triggering in Halshow. Both pins are providing 24VDC when triggered.

Once I reconnected the wires and tested again, the router circuit now works as expected, but the dust collector circuit gives me a "Smart serial card remote error = (27) Over Current" error. I have researched this and I think my problem is that there is no flyback diode on the dust collector relay. Does this sound correct? If yes, can you tell me what diode I need to get and exactly how it should be soldered in?

Thanks

If you are getting over current warnings for Mesa outputs, the relay is way out of spec for current draw.
Having said that, any silicium diode will do, something like 1N4001 to 1N4007 will do just fine, wired in parallel to relay winding, just mind the polarity in regard to Mesa output.
I would use another smaller relay in between, or a transistor.