It's funny - originally I doubted the resistor could be the issue, but thinking about it and how it could really influence the capacitance of the circuit if open I convinced myself I guess.
So yeah, looks like that one little resistor is the problem - but you had already figured it out before I stumbled along.
I don't think it'll hurt anything to run it with the jumper, other than draining the battery quicker,
but I'd sure like a second opinion there. (if anyone has any suggestions I'd be open minded to hear them, thank you)
Ground loops? You're on your own!