I feel your H is really putting forth some effort to understand himself and try to figure out how to reconnect/ show he cares/ make amends. Please Google "bids for affection" and see if it makes sense.
When you ask, "why would he do this if he's not speaking to me/ we are not speaking to each other?" I wonder what type of response you are giving him when he does these things? Are you gracious? Appreciative? I see that you've said he still has friendships and flirty behavior with women. Is it possible that he just really enjoys getting positive attention from women because he needs it to feel wanted, masculine, appreciated as a man? If this could be so, I hope his "bids" for affection from you are met with sincere and welcoming appreciation. I haven't seen anything in DB or anything else that doesn't call for that. And nothing will cause someone to give up more than feeling un-appreciated...it plays into the need to belong and be accepted, and without that a person can feel lonely and worthless.
Guilt, by the way, is really strong with your H. Yes, you can forgive your H all you want for his behavior, but he has to be able to forgive himself first and foremost to feel worthy of being loved by another, especially someone he loves and cares about. Without forgiving himself, anything positive from you will feel false to him, even if he is hopeful. He needs to be able to feel safe and secure, to trust that he can really open up, most likely. When he can finally forgive himself, then he may be a bit more able to talk at appropriate times and in a more real way. I'm sure his being "not ready" when you got home was due to really strong emotion. He probably has to prepare himself to be around you right now. Emotions are such powerful,confusing, but very basic parts of our being. That was such a perfect "flight" instinct in operation. He does not feel safe yet.
As confusing as this is, this is on him. He does need to forgive himself. But you need to feel safe to him, too. That's why we need to be working on ourselves. Are you still bringing up the affair and reminding him that he hurt you? Trust me; he knows. Bringing it up over and over...well, my own XH would say, "stop beating me up!" That's exactly what I was doing. Stop it, if you are. At this point, its done. He knows he hurt you. He's ashamed, even if he hasn't apologized or doesn't "get it". If you get to a point where you really are piecing, only bring it up with an IC (preferably a therapist that you work through issues and histories with, not just someone giving "advice").
We as LBS need to understand our own emotions, especially anger. Obviously your anger is from his behaviour...on the surface. But what is even deeper below that anger? What is the source...how does it make you really feel? This is something to work through with an IC. This is the you working on you part. This is how you can be ready to "be the lighthouse" in that story. Otherwise, you're just hiding the rocks that he will wash up against. Right now, that might be his suspicion, and his fear. Even though his actions are showing that he hopes sometime to see you guiding him home to safety.
M-51 H-54 2D-27 and 25 M-26 yrs Bombshell and IHS 7-29-15 He moved out 10-3-15 D filed 1-27-16 D final 10-27-16