Do you remember the make/model of the old air handler? With any luck you can find a schematic and see how the AC receptacle was wired to the AH.
You will need a schematic of the new AH to know what possibilities there are for you.
One way you could go is by using a sail switch connected to a relay (24 volt coil) switching the 120 volts AC. Google sail switch to see some examples.
You could wire the R of the AH thru the sail switch to the relay coil and then to the C of the AH. When the sail switch closes with the flow of air through the AH, the coil will energize switching the 120 volts to the air cleaner.