My son is also the "stalker" LOL He waits to see the neighbor's van pull in the driveway and then he yells out the door "Hey L, can I come over and play" before I can even get to him to tell him no. I've joked with the mom several times about my "stalker son". I've just had to explain to him that he needs to give people a chance to relax and unwind when they get home and usually he just forgets to ask again later.
Also, he "stalks" our older neighbors on the other side. Every time the husband is outside, my son is right there at the fence peppering him with questions "Mr. G, can I help you water your grass"..."Mr. G, why are you raking your leaves"...."Mr. G, what are you reading"....I joke with Mr. G that my son is "Denis the menace" and he's "Mr. Wilson".
B., our sons are just really outgoing, friendly little people. But sometimes it IS overwhelming to shy or busy people. So try to speaking with the mom (she MAY not mind, but still, its a good idea to give her an out too) and also just remind your son that its being a good friend to respect peoples' needs for alone time. This hasn't ENTIRELY worked with my son, but it has helped to curb his stalking behaviors....LOL