I always believed that they prayed to Jehovah, and god would use his holy spirit to guide their discussions and influence their decisions. This would happen in a manner that couldn't be detected, you just had to trust that it was happening. One way to know that it was happening was that the guidance from the GB would be reliable and true. Which is why it's such a problem when their guidance is so unreliable that they must state that they are fallible and can get things wrong.
Look, we know that they are 'just fallible men who can make mistakes.' But they claim to be the head of an organization that is led by Jehovah himself and they frequently remind the rank-and-file of the importance of obeying the GB no matter what. If you claim this and you still get things wrong, then there are two possible reasons for it. One: Jehovah is either being deceitful or incompetent. Two: You don't have god's favor and your claims are false.
I'm kinda leaning towards two.