I am INFJ; he is INTP. I think the main way we reconnected was that we never stopped talking, and we always support each other as friends first. Every relationship is different, and though people may seem to fit into a certain type, everyone is still different. That said, in my situation, we were much younger (late teens - early twenties), and I initiated the breakup when I wasn't getting what I needed from the relationship; I worried about how young I was and how attached, yet lonely, I felt much of the time. We were only apart for a few weeks, but I still called him everyday, and he always took my call - he played the role of my best friend, not my ex. He helped me work through my own fears, and feelings, without interjecting his feelings, or persuading me to see things his way (though I know he was hurting). Sometimes we just talked about what we did that day, and didn't even discuss our relationship. We eventually agreed that we were happier together, and agreed that communication was was key for us, so that things don't build up until the dam breaks (it's hard work, but worth it).
There's no formula for how long to wait before reaching out. When I say to give each other space, please know that I don't mean to stop talking. I mean that not every conversation has to be about your relationship, or trying to convince her to forgive you and take you back. Personally, I think that's asking a lot given that you ended the relationship and it was months before you reconnected. Yes, you should say that you're sorry for the breakup and make it clear that you are happy to reconnect, but don't push for more than that right now. While it is promising that she is responding to your messages, I think you run the risk of pushing her away if you pressure her for a decision she's not ready to make.
Were you friends before you started dating? If so, trying going back to that and replicating your connection from that time. I say don't focus on the past, or the future, at this point. Focus on the present. If you focus on what connects you right now, and enjoy spending time together, maybe you can build upon that, and the future will become clear and start to feel achievable.