Ford E-series generally have all the accessory/lighter sockets on all the time, at least so far as I know. Certainly mine are both always on.
It would not be a particularly difficult job to add a relay to turn one off with the ignition using e.g. the switched lead for the radio, which is conveniently in the area. (Actually, for dedicated use by a dash cam, wiring up a new socket to that lead would also be fine; a dashcam doesn't use much power.) I think some dashcams also can be set up to turn on and off based on movement rather than switched with their power supply.
If you have a front window on the cabover, that makes a superior place to stick a dashcam. It's out of the way of the driver, and gets a very nice view of the road.