I don't think a thank you note is pressure.... just a quick, "Hey thanks for the _____. Take care, Your name" that's just being polite. That's something you might convey to anyone.
I think it's okay as long as you don't add any "love" words or mush. Just a nice polite acknowledgement....
BH, the reaching out 1x for every three of his is wise. BTW, I too had little DB "goals." For example, I remember one of those goals being to get him to call me, another was getting him to invite me to do something. They were always very small, gradual, and one-step-at-a-time.
There is no arriving, ever. It is all a continual becoming.