Sounds like as you say a permanent live from the ignition, for an immediate cure, fit a switch in the wire on the dash to isolate the feed.
Not up on defender wiring myself, never played with one, but if its like rrc wiring there normally is only 3 or 4 wires out of the back of the ignition block.
Again going on what i've seen if it is this type of unit sometimes the electrical block on the back of the igintion switch unit comes loose and can twist, so even if you turn the key off not all the contacts break the connection, you can have a look behind the column plastic to where the barrel unit is