Hi,
If I am understanding correctly, your best path forward is proper queue "Destination if no answer" setting, where you point this to whatever is your alternate pickup option - other queue, extension etc.
As a first point, for queues to work optimally, members should be logging out if they are not at their desk so the call can be sent to the next hop directly. Otherwise you can make sure the queue timeout is appropriate.
And with update 9 you can manage such scenarios within each queue itself using the cumulative strategy (
https://www.3cx.com/blog/releases/call-center-queue-features/ ).
All the above do not depend on someone hearing a phone in the distance or noticing a light has been blinking for too long, but your fallback answerer get's a proper call.