I see your point MtlBiker. Running from the cops takes more than being able to turn your GPS off but I do find it slightly annoying that I have to wait 30s to tell the GPS to stay on (those times when I want it to). For me that still wasn't worth drilling my headlight cover but that's a personal choice. Gambeaux, MtlBiker already answered your question. No power draw worth speaking of on the trigger wire - a few 10s of mW maybe.
"Rumors of my assimilation are greatly exaggerated." (Capt. Picard)