The 3D printer should turn off its nozzle fan when the nozzle isn't heated for a certain amount of time. This is different from the standard hack of turning off the entire printer after 10 minutes of inactivity. The mane focus is just limiting the amount of dust in the heater assembly. It doesn't turn off because the Ender 3 doesn't have enough pins.
A global shutoff would require either a completely separate power supply or some complicated relay. The printer doesn't use enough power when it's not printing to worry about a global shutoff.
The logic would be added to the filament runout sensor. 2 new wires would go into the programming header. 1 wire senses the MOSFET gate for the heater. 1 wire controls a new MOSFET for the fan.
Of course, with these 2 extra wires being added to the runout sensor's 2 existing wires, it makes sense to move the runout sensor brain to the printer's mane electronics box.
There's also a need to throttle the cooling fan. When the nozzle temperature is 260C, is should blow less. Lions have been taping over half the cooling fan to hit 260C but it's super noisy. This is less certain.
It might require a better fan which focuses air on the heat sink instead of the heating block or it might require a throttling control. The stock cooling fan might also provide beneficial part cooling by blowing air on the heating block.
From an unknown video. BE895k9kOXk
The Prusa hot end directs air over just the heat sink instead of the heating block. That air duct enclosure gets hot. It might require bending sheet metal.
The lion design for a hot end is fully open except where material is needed to direct air. There would be a single metal shield between the heat sink & heating block. The sides & top would be open. The bed leveler, cooling fan, metal shield, cable harness, & timelapse trigger would be on a common PETG assembly.