I have a universal 25XP. With my ignition switch off I will sometimes get a low oil alarm and my fuel pump will operate as if the key is in the on position. I have replaced switch so that is not the problem. Possibly Ithought maybe I was getting a back current from the alternator ,as in bad or weak diode allowing current to run in wrong direction, but believe that is not the case as problem is intermittant.
I can't figure any other way this line is being powered when it clearly should not be. I have noticed that the last time this happened my RPM gage went nuts so this must also have been powered as well and would run both clockwise and counterclockwise.???
Next time it happens, with the engine stopped and the ignition off, take the big positive lead off the alternator and see if it stops. If so, you know something is amiss in the alternator wiring circuits. If not, look for problems elsewhere, including incorrect wiring, possible damaged/shorted wires in the harness, etc.
"take the big positive lead off the alternator and see if it stops"
I'd add the warning that that lead is HOT AT ALL TIMES normally, since it runs right to the battery positive. So it should be handled with caution, as it will try to short out through your wrench and either blow a fuse or slag a wire down.
Folks tend to forget that, until the sparks fly.