Power failure relay options

What if the power comes back in during the 5 minutes between 1) and 2)? Do you want a reset or continue with the 12V relay? How do things get reset when power comes back on after 5 minutes?
And so on... You have to address all the scenarios to better design the function you want.
Simplest is use a 240V relay that drops when power is lost and engages the 12V circuit. You then need a 5 minute timer (powered by your 12V) that triggers a second "one-shot" (2 second) timer for your mechanical switch.

Thank you so much for taking the time to respond. This widget is to restore mains power after shut down by trip switch; thus, power will not come back on until 1 + 2 are completed.

Your suggestion seems to be more or less what I outlined. I am wondering if it is possible to do it with a single widget, i.e., a single unit that senses the mains power outage and does not trigger the switch until 1-5 minutes later (5 would be nice but 1 will do). Alternatively, this could all be 12V - i.e., 12V power brick into mains socket powering widget, widget senses when incoming 12V goes off then starts? minute delay before triggering relay...? (Circuit would include 12V battery to power widget when mains power to power brick dies.) I suspect my terminology - and ignorance - will be making many wince, for which I apologize!