The optic is designed to do exacty what you describe. I don't think the holster matters. So you are correct, when seated (Little to no movement) it turns off after approx 2 and a half minutes.. When you are carrying you are moving enough so it turns on..Been carrying my 320C RX/SC for awile, decided to keep track of the dot while the gun was holstered. When Seated the dot turned off like it was supposed to. However when walking or moving the dot stayed on a lot of the time. In fairness, I am using a holster the covers the sight and was made for an RMR which is a tenth of an inch less wide so the sight touches the kydex in a few spots. Also, the holster is for a railed regular compact and I am using the compact slide with the sc grip module since Sig doesn't find it important to actually make 320 parts available, at least grip modules and some mags). I have a regular 320C RX holster ordered and I'll see if that makes a difference. Still, this could be why some get three weeks of battery life and some get several months.
I would vernture to guess (Barring any extended periods of standing still), it would stay on damn near constantly when carrying.
I am not convinced the battery life is a week with it on constantly as there are plenty of folks that indicated they have had it on for months and still going.. Alot of those folks carry. I bought mine little over amonth ago and the battery is still going strong.