In a former life, I was a cop. In my state, traffic control devices (stop signs, one-way signs, etc.) on private property are not subject to the state's Motor Vehicle code unless the property owner grants the police the authority to patrol and write summonses (and the signs must comply with state standards). We had a big mall in our town and the mall wanted stop signs enforced (and they wanted cops patrolling), so we wrote more than a few stop sign tickets, but generally only when an accident occurred.
And yes - full and complete stop and you must yield to oncoming traffic. Easiest way is to focus on the rims, not the bumper. Much easier to catch the slow roll. Around here, people approach the stop sign with the intent to merely slow down and only stop when another car is coming. As we used to say - all you need to know is written on the sign: STOP. No asterisk for *if no one is coming, *if you feel like it, *if there's no cop around, *or go slow, that's fine, too.