pressure switch, is what ya talking about. that kicks on/off the pump when air pressure gets to low / to high.
i would imagine, if you double checked amps ((starting amps)) NOT running amps. and then obtained a "pressure switch" that was able to handle that many amps. you could wire both pumps up to same pressure switch.
that or perhaps a couple relay switches. that would kick on the pumps when pressure switched turn on and off. though if you could add some sort of delay so both pumps would not kick on at same time. but say 2nd pump kicked on a minute or so latter. you would most likely be better off.
as far as duty cycle. ((running constantly non stop)) you need to be very careful on shop air compressors. they will heat up to point of breaking. if you see some sort of cooling fan blowing across the motor, you will more than likely start seeing longer duty cycles if not contentious running.
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regulator is what controls amount of pressure. example tank has 120 psi. but the tool you are using you only want a constant 60psi, the regulator makes this happen.