When you pull the air-gap which terminals are being disconnected

I’m having a problem where my light bulbs are staying on dimmly when in an off state. I had the same problem with the previous dumb switch as the Black on/off i installed so I had assumed it was some kind of wiring issue outside the gang box. When I pull the air-gap for the switch though the bulbs turn off.

I had assumed the air-gap would just cut the power to the line terminal, but is it also cutting the connection to the load terminal?

You can’t cut power to the line terminal as the power is coming FROM the line terminal. It cuts everything downstream of the line terminal INCLUDING the load terminal.

I meant i assumed it cut the connection between the line terminal and the rest of the inner workings of the switch.

If it is cutting the connection of the load terminal with the ground terminals then that might explain why i’m seeing this behavior.

Yes, it should be cutting power to the Load terminal. While we often think of the air gap as a way to reboot a smart switch, the original purpose I believe is to provide a safety mechanism for when the light bulb is changed. Not every smart switch uses a relay where such a gap is automatically provided, as some of them are switched via solid state.

Presuming that your switch is wired correctly, I think what you are seeing is a bit of leakage combined with LED bulbs that illuminate at very low thresholds.

Yes, that is correct.