The way I understand it is they get an overwhelming feeling to be with Christ in heaven as if they belong there. Kinda like wanting to go back home after an extended vacation. I've heard that members will also get the same feeling as they read bible passages speaking of the calling as if they are reading a very personal letter from an intimate friend.
This differs than the feeling when holy spirit is at work in someone. When the holy spirit is at work in someone it feels like an adrenaline rush where anything is possible. At least its felt like that for me.
Sorry, didn't even answer the original OP question :-)
The GB cannot possible have the heavenly calling with the way they have twisted scriptures and continue to promote false dates such as 1914 and the generation teaching, etc. Scripture is abundantly clear on this. Whoever speaks in God's name and it does not come to pass is a false prophet. I believe they are just holding onto power by force claiming something they are not. Power corrupts absolutely.