Mate I've clocked this too and it proper freaks me out every time. Doorways are basically just thresholds aren't they, boundaries between one space and another, and loads of cultures throughout history have treated them as spots where the veil between worlds is thinner or whatever. Could be total coincidence but it does seem like a remarkably specific pattern for something supposedly random.
Had one myself about three years back at my mums old house in Broughty Ferry, standing dead centre of the bedroom doorway just watching. Never came in, never left, just stood there. Still gives me the creeps thinking about it.
Anyone else notice they never seem to move toward you from a doorway, they just sort of stand there like they're deciding something? Curious if thats a consistent thing or if I just got a polite one.