A belated "Merry Christmas" to yourself and the lovely Mrs John T!
The cutout on my old Minnie Mo U - which I think is the same as used on the Allis G - has 2 windings. It works like this:
The 1st winding is many turns of relatively fine wire. It is connected between the generator armature terminal and ground. This winding senses generator output voltage. It "pulls in" the relay when gen output reaches 8 - 9 volts, thus connecting the generator to the battery so the battery is now being charged.
The other winding is several turns of heavy wire wound on the same core as the 1st. It is connected in series between the gen output and the cutout "BAT" terminal thru the cutout contacts. When the cutout contacts are closed, full generator current passes through this winding.
Now when the system is charging, the magnetic field of the 2nd winding adds to the field of the 1st winding, helping keep the cutout contacts closed tightly. However when generator output stops (ie. at slow idle, or when the engine is shut down) current thru this winding reverses - ie. battery is now discharging back thru this coil to the generator. The 2nd winding's magnetic field is now OPPOSING the 1st winding's field. The two magnetic field cancel each other and the relay spring causes the cutout contacts open.
Now as a practical matter, a mechanical cutout relay can be replaced with a solid state cutout (no moving parts) for about $35. No more fussing with erratic relays! Agri-Services has them - stock #GDR6030. Or try at any good starter/alternator shop.