I can understand your reluctance to bring it up but you're tormenting yourself over trying to comply with a "rule" that your T even breaks occasionally. I really don't see the problem as being entirely yours when your T doesn't always follow his own rule! On the other hand, it is possible that he will say that you can't send any email at all if you try to talk to him about it, so I guess you need to decide if that would really be worse than tormenting yourself over your difficulty with this boundary.
I think that you can still accept the reality that your T can't always be there for you while still being allowed the opportunity for some kind of connection between sessions with the understanding that he may respond rarely or not at all. It doesn't have to be so black or white. My T had never used email with a patient before I asked him about it, and now, 7 or 8 years after he decided we could try it, he uses it occasionally with other patients as well. I don't know why you are in therapy, but some people do need additional support between sessions. Email can be problematic but it also has much value in maintaining a connection for patients who struggle with the therapy relationship.