Be consistent in the way you react to a child’s behavior. Be strict or be easy, but don’t suddenly be strict about something you’ve always been easy about.
Young children I agree with presence and not just in body but in mind and spirit.
Older children, still important to be there but I think totally accepting your children for who they are becoming empowers them to be the best they can be.
Being present is important, no doubt about it. But I’d replace that with being “involved”, because it’s just not always possible to be present, despite the best of intentions.
In any case, I’d say that the most important thing is somewhat different: Set a good example. In other words, live the life you try to teach your kids.
I’m not a parent, but from what I’ve seen and heard from kids that I’ve worked with or mentored in some other way I would state these three things:
1. Communication and availability (as mentioned in the OP)
2. Excepting them for the person they are rather than expecting them to have the same beliefs/interests as you (the parent).
3. Actually caring about the child’s welfare, and making sure they realize you care about them.