Trespass is a tricky area. You can't simply seize someone for being on your property. If that was the case you could lock up half your neighborhood. You can ask anyone to leave for any reason whatsoever, its your property. But if they refuse and lets say they aren't doing anything, just not leaving... call the law and let them deal with it.
When you make the decision to hold someone at gunpoint, it better be a situation where you were in fear of imminent bodily harm. Especially when outside your house, even if it is inside your fenced in yard.
It is quite common for bad guys to call the police and report “a man with a gun”. Even if you do not display it of course because they are well...bad guys and you scared intimidated them and they want to get back at you.
They do so also in an effort to cover their a$$ and to get back at anyone having the temerity to chase them off.
Some people recommend you immediately call the police. That's up to you. That course of action has it's own pluses and minuses.
I think the best advise you were given here was to note the individual.. Observe him, try not to be observed yourself. Certainly do not open the door and engage in conversations or anything else (You have no idea if there is one or five people out there.
You also should not be the only one in your house who is assuming a defensive posture.
States like Arizona allow for defensive displays but they are still a poor idea.. because of the enemies false allegations.
You need to know the laws of your State. You need some SOPs worked out in advance when your not worked up to guide your decision making process.
These are not questions and answers you want to guess about or try to figure out on the fly.
W