LM555 timers for control of a secure door
Assuming I am not miss-understanding your requirements, you ought to be able to do this simply with one 555 and a couple of MOSFETS.







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How that ties into the rest of your circuit is anyone's guess though. If the door open switch is already being handled elsewhere then either bring the signal over to a parallel MOSFET as shown below, or diode OR into the gate of M1 with an added pull-down.







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simulate this circuit