Why not (cautiously and politely) flag him down on one of his loops and act like you're just trying to be helpful (Are you looking for someone?, need a place to wait to pick up someone?, Trying to decide whether to come in or not?, etc.)? We do that all the time on our team, and it seems to clear up situations without making someone feel unwelcome.
Until I started serving on our church security team, I never realized how strange "normal" people are. Guy came to the service with a suitcase this past Sunday. Sat on a bench in a hallway outside the sanctuary, never went in. Left his suitcase unattended to go to the bathroom, and one of our folks approached him to start a conversation. Said this was his family's church (but not his), and a cab was coming to pick him up to go to the airport. So many why's there.
On a Saturday a year ago spring, we had training for a children's ministry volunteers. They asked 3 of us (security) to be there till 11:30am. Guy drove up and parked in a central location and just sat in his car. Made one of the rovers suspicious, so he wandered in the car's direction. Guy started up and moved to an overflow lot as soon as our guy got close. Rover walked that way and guy did the same thing, but moved to the other side of the campus. Rover got me to get a second opinion, and I thought he was probably being paranoid. As soon as I saw where the guy parked, I knew he was up to no good. In an almost empty parking lot that holds hundreds of cars, he choose the only spot that was covered in 3 directions and allowed observation of the church. Rover circled around one way; I went the other. He watched the Rover, but didn't see me. Got about 5 yards from his door in his blind spot, and as soon as he saw the rover getting close, started up and backed out. He was visibly surprised to see me standing pretty much next to his car at this point. Definitely wasn't happy about the situation, so he left the property this time. Got his tags and BPD said he was a known member of the Kurdish Pride Gang (defunct now I believe). Nothing ever came of it, which is great, but the randomness of it was strange. Educational though.