Possible to use NC/NO switches as 3-way switches?

[thevillageinn]

Hello everyone,
I'm trying to learn whether I can wire up a couple NC/NO switches to act like household 3-way switches on a gate controller? I tried as many combinations as I could guess at the other day and wasn't successful.

The back story:
Where I work we have a privacy gate to the entrance of the property and while we have a strobe sensor to open it, it also has a bypass key switch which the local sheriff and fire departments can use to open the gate. They have a key to that switch - I do not. I can open the panel the switch is installed in and access the wiring and rear of the switch. The key switch seems to be a NO/NC switch with 2 of the 3 pins connected to the gate controller board. Should the responders use the key bypass they usually leave without closing the gate - then we need to wait until they make a trip out to close it - which is a waste of time and effort.

I'd like to have a second switch which would essentially swap the state of the key switch and allow it to function for them and close the gate for me...which is why I am likening this to a household 3-way switch setup.

Any thoughts on this? When I was somewhat successful, I could get my second switch to reconnect the circuit but the first switch would not open it again.

Thanks for any assistance.