With a current that high looks like a relay may be stuck. A relay is a device where you can switch a very small current via a small switch to a magnetic coil ( often 50millamps or such ) and the magnetic coil attracts an armature attached to heavy electrical contacts capable of switching over 40 amps typically. The feed to the coil ( the control signal ) is fed via a small switch on dashboard or on steering wheel stalk and 'relays' the signal to the device you want to operate ( heated screen, headlights, aircon system etc ) - the power to the the switch that operates the relays is fed via the ignition switch, so disappears when ignition is turned off. However the feed to the heavy relay contacts comes straight from battery via a fuse and is still live when ignition is off. The heavy contacts are supposed to be opened with a spring when no power to relay coil, but sometimes the armature sticks and contacts stay closed, this can keep power flowing from battery to the load even with ignition off. Aircon clutch can draw 3 amps, headlights 10 amps, heated screen over 10 amps etc.
You need to locate relays in fusebox and while someone watching the ammeter pull them out one at a time and see if the load drops. Problem is that often the relay will not stick every time but do so occasionally - which makes it pot luck if you can find it - the relays are not normally expensive though and maybe on an older car may be due for replacement anyway as a precaution.
