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I am not where I can currently look at a diagram. Also I do not have a Toolroom anything.
Almost certainly your Home Depot pump is single phase. Probably also nominal 120 V AC 60 Hz. You need to know the HP rating or current load of this pump when pumping.
If HAAS uses 120 V single phase for the coolant pump, then if you have the same motor rating or lower power you should be able run from the same source as HAAS uses.
Is the Toolroom Mill a single phase or three phase unit?
Look in your manual to see how HAAS connects the coolant pump. Since the TL-1 can be single or 3 phase I suspect the coolant pump is single phase. This would reduce the number of spare parts. This means you need to determine the voltage and power rating of the HAAS pump motor.
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