You don't want it connected to a permanent live fuse. The idea is that when the ignition is off, the internal battery of the camera powers it up in the event of a bump etc on the car.
This is true to a degree. However the penalty for not having it hard wired in, is that you have to use the cigarette lighter, if you have one, as a power supply.
Or a 12v outlet close enough to the dashboard.
This means that you will have some cabling in view and not be able to use the lighter should you need to. And to be honest, it's an eyesore.
The Dash Cam will automatically power on and be ready to use once power is available.
In some vehicles this will be when connections are made, for others the Dash Cam will power on once the ignition has been turned on. Mine comes on as soon as I open the door and the room lights come on.
When power is cut off, after a time lapse, the Dash Cam will perform an automatic shutdown process and fall back on the internal battery.
If your camera has the facility as mine does and Intelligent Parking Mode is active, then when motion is detected, it triggers recording automatically using the camera internal battery.
The battery will obviously recharge when 12 volts becomes available.