What exactly are y'all suggesting he call the cops for?
I'm imagining how this phone call might go...
"Hello, 911. Please state the nature of your emergency."
"Well, someone rang my doorbell. And then they waited to see if anyone would answer! And then when no one answered, they rang the doorbell again!"
"Okay..."
Be cautious? Sure. Put up a sign saying the previous tenant has "moved on"? Sure. Calling the police because of behaviour that is perfectly normal, save for the hour of the day? Maybe not so great. After all, the guy did just go away after he didn't get an answer.
As for those suggesting he shoot the guy just for ringing the doorbell early in the morning, seriously, folks. This is the High Road. Let's not be our own worst enemies.