Sending units are potentiometers that vary according to fuel level.
Ford sending units (and Chrysler for that matter ... GM is exactly the opposite) display their highest resistance (around 74 ohms) when the tank is empty and lowest (around 5 ohms) when full.
If your Comet is like my Tbird, there's an access cover in the trunk floor to the sending unit. There should be 2 wires running from it, a ground and a gas gauge wire. Disconnect the gas gauge wire and see what your dash displays ... it should show an empty tank (ie; max resistance). Then touch this wire to ground (briefly, so you don't harm the gauge) and it should read full (ie: min resistance).
This will confirm the dash gauge and wiring are good and the problem is in the sending unit.
I suspect there's a short in your sending unit that only allows a maximum of say 35 ohms (1/2 of max resistance), hence the 1/2 full tank on the dash gauge.
Now why it makes a difference in acc. versus run, I don't know, this is the extent of my knowledge, based on the work I did on my Massey and Caddy fuel sending units.
Hope it helps.