You had your present alternator rebuilt? I might disconnect the alternator heavy feed wire and insert the ampmeter in the line. Thinking maybe a leaky diode in the alternator. A rebuilder would not miss a shorted diode yet could miss a mild leaky one. They do not always totally short.
If the welding was done without proper precautions electrical wise it could have easily started a problem.
Simple stuff first make sure things like the trunk light are really out with the lid closed but a systematically removal of all the fuses should have caught that. You are basicallyleft with things that do not turn off with the key switch and as someone mentioned the security system might be suspect. With out a wiring schematic it might be difficult to isolate. Does the glove compartment light act independently from the key switch?