Well that is a very interesting question. Thank you for asking.
Connections are important, yes. For me family is the most important because I know that no matter what they're going to be there. Friendships are a little different. It depends on how you use the word close. I love having a lot of friends. I love having good friends. I would say however, that there are very few people in my life who I share emotional stuff with. Half of these people are my family and the other half are people that I really cant explain to you how i ended up being so close to them, it just happened. We love the idea of friendships, we do what you do in that we stand by someone completely and will always offer support and advice. But I have to say, for me personally i really dont have very many close emotional connections with people because I honestly dont really like them. I have one with my mom and my sister for obvious reasons and then my best guy friend, who just happens to be an ISFP. Oddly enough both my mom and my sister are also FP's.
I like people who will listen yes, however, I cant say that I'm big on emotional support. I know that sounds pretty heartless, but I really feel vulnerable around any kind of feelings and so if I do happen to tell someone i dont normally share things with something really emotional I tend to not talk to them for a while, or just pretend like it didnt happen. ESTJ's do not like to be emotionally pursued in any way. We dont really like to talk about emotions and so trying to get us to makes us close off really easily.
I have good friends who I hang out with, joke with, live with, and do a lot of things with. We talk about almost everything, but in terms of my deep emotions or if I get upset, I would rather be left alone with those things than talk about them with someone. It sounds bad, but it bothers me if someone is trying to get me to tell them why i'm upset. I tend to surround myself with introverts, because they usually are less invasive.
Friendships to me are very black and white. Either I am friends with a person or I am friendly with a person. There's really no in between. For me family is something that is permanent and friendships just sort of drift in and out. I know often that people think they're friendships will last forever, I know I have, or that they will always be the way they were, but the fact is that people grow older and become different and move on the different things constantly. So unless they're someone you're going to spend the rest of your life with (like a spouse), you have to assume that there may be a chance that it only lasts as long as its going to.
However, friends for me dont go away forever. I can easily be really good friends with someone, not see them for several years, end up in the same place again, and become good friends again. It all depends if I still have things in common with them. When I feel we are drifting apart a little, its a little sad, because it was a large part of my past, but really, I dont feel like there's anything i can do about it. If I wanted to still be good friends with someone I'd talk to them more, especially if they're in the same area as me. It is very rare for ESTJ's to break good friendships for random reasons. If there's a problem, we have no difficulty seeing it through, running is really not our thing.
Its interesting that you bring this up now because I'm actually feeling separation happening from a friend I had for about 6 years now, and recently I feel like she and I just dont have as much in common and that I at least need a break from her. To be fair though, she's being really controlling of me, and is bashing my other friends and then denying that anything is wrong when i speak to her. For me, I'm really trying to help her and fix whatever is going wrong, but if she wont tell me anything and continues to be rude and control me, then I'm going to shut her off little by little. I know that sounds mean, but I guess its my protective strategy.
The fact of the matter is, we dont like to talk about feelings. So if I was drifting apart with someone suddenly or not talking, I either dont notice very much because I can always jump back into friendships easily, or I wont say anything because I think that we just clearly dont have as much in common anymore, or if I thought there was a problem I'd say something. It wouldn't be in emotions or feelings, but it would be in facts, like such and such happened what was going on there? or you're doing such and such to me. We have no problem being critical with people, so you're going to end up hearing if something is really wrong probably in a harsh way, but it'll be said.
You might want to talk to this ESTJ. We are completely open to direct confrontation so feel free. Its possible this friend of yours might say "oh i didnt think we were drifting apart", which then you need to explain why you feel this way so that it can be fixed. We are fabulous at fixing problems, but only if someone actually tells us there is one.
As for an emotional connection. If you dont feel you have one with this ESTJ, most likely you wont have one for a long time or even at all. It takes a lot for us to really open up to people, and I have to say that I tend to open up to IP's more than anything else. Try not to be an emotional pursuer, it sort of turns us away a little bit, we dont like that kind of pressure.
Feel free to ask anymore questions. I'm sorry for such a long answer. Hope this helps!