Carrier Gas Furnace - Humidifier Condensate pump

[Marcplante]

Question:

Are condensate pumps typically powered by outlets that are tied to furnace power?  To save electricity? maximize pump life?  It seems like the pump would need to work FTTT after the furnace has finished to drain residual.

Background

The condensate pump on my carrier furnace has been acting up, (leaving puddles on the floor) and I suspected the float switches were done (It's 11 years old).  The furnace has an Aprilaire humidifier panel, so this catches overflow and pumps it to a laundry sink across the cellar.  The new pump install went fine (Basic Everbuilt pump from Home Depot), but I was wondering about something.  The new condensate pump I installed has a power indicator light. When I plugged it into the outlet, the power light did not come on.  I plugged it into the outlet that the humidifier panel was plugged into, and the power light came on. At that time, the furnace fired up, and I unplugged the pump and plugged it back into the outlet designated for it next to the furnace and the plug was powered.