I wonder how long before boarding gates close last calls are first announced. E.g., is it 15 minutes, 30 minutes prior to the closure of the boarding gates, depending on the boarding staff's mood, the airport, or the airline's policy.
The airline will close the gate at the gate closing time stated on your boarding pass. That's the only thing that matters.
"Last call" announcement are entirely optional and there are no specific rules or consistent practices that are employed. Mostly it's done if a passenger is late that has checked luggage. The airline will typically try to call them since otherwise they have to unload the bags which is a pain in the neck.