Thanks guys!!
Klaus, my trailer connector is configured differently. From the drawing you provided, my ground is in position "C" (8 o'clock) and battery is in position "F" (2 o'clock). This is both as diagramed on the cover of the connector, as well as verified with a voltmeter. All other positions are not powered with engine off.
Perhaps an 04 difference?
Though my Stud 1 also just had that plastic plug cover...
Paragon, I need this power only 20-40 minutes, once a month (at most), just to hook up my portable compressor when airing up -- hate the idea of having to run a dedicated new wiring for that...