Brad - here's what I think:
I think this is a default setting for him. He's gotten what he's needed in past relationships (probably even with you) by withholding attention, conversation, etc. to entice you to go to him and ask what's wrong and try to fix everything. That way, he gets the attention (albeit negative) that he desperately needs. The staring is to make sure you know he notices you - also to confuse you and perhaps get you to come TO HIM.

Your indifference and lack of contact is probably confusing HIM and he may try a new tactic after awhile. He is trying to gauge where you are emotionally and figure out what his next tactic will be. I don't remember the circumstances surrounding your breakup but if YOU were the one to break up, he's probably also playing the "injured party". He may want you to think that you've really hurt him so you'll feel guilty.

I firmly believe (from my experience) that they want and need to have complete control and power-over in the relationship - even post-relationship. So whatever tactics they can use to make themselves feel in control, they'll use. If he approaches you to say hello, I think he would feel like he's caving and giving you the power.

At least that's exactly what my exN is doing and I think our situations sound very much the same. The sad thing for me is that toward the end of my relationship, I became aware of the "power struggle" and allowed myself to get caught up in it and act as he always acted. I became determined to not give into his games and end up feeling powerless again (and doing this, actually become more caught up in the "game"). The best thing is probably to not try to figure it out and just avoid him as much as possible.

Just my two cents...

Well if you read my story in order to understand more about my situation,he asked me to leave then to stay...many many times in 2 months...but because i couldn't stand anymore the punishment ,the gaslighting, the push and pull and the day before i made my decision was another day that he didn't talk to me all day,incluiding at the supermarket doing groceries and if someone spoke with me,he just walked away....so i also kept silent,my heart was bleeding inside...it was beautiful weather, i had waited to be with him for 2 years and when i got to the usa thats what i got...(please read my story)...but in the evenig(after groceries he went gaming the hole afternoon and evening)sudenly he came to the room i was in watching a movie on my laptop and gave me a hugh(he did forbbid me to touch him,only he could initiate any display of afection)and said please stay until new years eve we can have a wonderful christmas together and is goin to be fun cooking,etc....And this he tells me after telling me inthe morning that he want nothing to do with me and that would be better if i left for Europe....so i was sad confusd tired and for me was very very difficult to see the man i waited for 2 years,so near but so distant and so disordered....i was getting very very sick....phisically and mental...so i said ok i stay...but the next morning i woke up ,called the airlines ,he got out of the shower and asked me who i was talking to....i said the airlines i made changes i am leaving in a week.....he got very quiet,went to work but came back during lunch....and all he did was look at me....with a shirt with a lipstick mark on it....i didn't ask him anything....he was very quiet the entire week,when i left he wanted me to keep his home key i said no....i said i hope we will stay friends...he said no,i will call you once when you get there and you will never hear from me again....he is NC on me,but he did sent me 2 emails saying that he doesnt want to have conversations with me but wonder how i was doing....and the other one was that he was sure that one day we will become friends again ,only without the high expectations we had for each other....i did called him,sometimes he did talk to me,calling me names,telling me a lot of confusing and sad stuff(that he maybe was gay)then he wasn't told me to jump in front of a train and then called my sister in Brazil and told her i was about to commit suicide...and he is NC on me and i am NC on him.....what i want to say is he wanted me gone then not and when i went he started punishing me...he told me from now on you will only pay and pay.....