A while back a thread mentioned an automatic switch from sears
It has three 110v receptacles. When power is drawn from the master
receptacle, the other receptacles are switched on.
This makes it useful for turning on a dust collector when some other
tool is powered up.
The original thread discussed a problem in which the circuit in use
could not deliver enough power for two tools at once.
I responded with a description of how an external relay could be used
to switch another circuit. McMaster-Carr #7678K62 DPST for example.
Anyhow, I got one of these switches & looked inside; it contains a
SPST relay that is thrown when current flows through the master. It is
possible to rewire it internally so that the relay switches another
circuit. The two circuits must share a neutral.
An external relay is probably a better strategy.