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You could probably use 2 common relays:

1st relay would be powered up by closing circuit no. 1 using the coil of the relay

2nd relay would be powered by the 1st for the function of the circuit in question

both circuits would have to be closed before the 3rd circuit would close and function

I thought of a much simplier way to solve your problem.

Get a cooling fan relay at

Auto Zone Part no. 19899 $15.99 and wire as follows:

Terminal No. 85 power up when circuit No. 1 is activated (turned on)

Terminal No. 86 Ground

Terminal No. 87 power up when circuit No.2 is activated

Terminal No. 30 Load of circuit No. 3 (the one you want to control)

I think this will work for you

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Q: How do you wire a circuit to close only when two other circuits are both closed?
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