Dual HVAC System with Dual UV lights - looking to power UV lights when HVAC runs
The wiring diagram for the Amana unit appears to show a connection for an optional mains-powered electronic air cleaner. This might be just right for your use. You'll have to find literature from the furnace to confirm how much power that connection can support, confirm that terminals you can use are available on the circuit board, and confirm that the power requirement of the UV lamps is compatible with what the furnace control can provide.
The Carrier unit is a little more clear about its support for an electronic air cleaner. The legend printed under the wiring diagram shows terminals EAC-1 and EAC-2 are for powering an air cleaner at 115 V with current up to 1.5 A. I'd guess those terminals are going to be 1/4&quot; blade quick-connect type.
For both systems you'd have to check the manuals, or simply experiment, to discover when the control turns on the EAC output.