Mesa 7i76E Relay Selection?

I would like to implement a Hand-Off-Auto switch for 110VAC vacuum system, e.g. Shop-Vac, and a second for 110VAC cooling system (water pump) for spindle.  Mesa tech support recommended I post here on LinuxCNC.

I have a Mesa 7i76E with 24VDC control circuitry and need advice on the type of relay to acquire and how to make the wire connections.  I watched Rod's "Spaceship Plazma Scratch Build" on YouTube and from it I am pretty sure I want to stay away from mechanical cube relay. 

Thank you in advance.

It depends on your current requirements.
I did not show it in my video but I have used these with a 7i76e
oceancontrols.com.au/KTD-273.html#produc...ls-tab-specification
For bigger currents, something like this
www.jaycar.com.au/solid-state-relay-4-32...a-switching/p/SY4084
you can get heatsinks with builtin din rail mounts for this style

Thank you. The pump is a simple submersible aquarium pump, 120VAC. The label on one states 75W (0.625A) and on another unit states 100W (0.83A).

Looks like the Ocean Controls relay would work for both. With that solved, how is an HOA properly wired and triggered from the Mesa 7i76E? Would the +24VDC from the 'Auto' side of the switch go to a Mesa board input pin which in turn enables the relay via an output pin? I presume the 'Manual' position bypasses the relay but with no "signal mechanism" I am not sure how it gets wired up.

You are triggering a relay so you need to use an output. Connect it to the relay + input on the relay and the other relay terminal will go to  field power -ve
Normal relays would see us add a flyback diode but being a SSR, I don't believe it is necessary with this relay but it should not do any harm.

My video gives an example of this