Personally, I do believe that Randall became more than just sex. Jack wanted to share a life together with him. The only other person he asked to do this with him was Ennis.
Correct me if I'm wrong, but we don't know that it was Jack who asked Randall, do we? I can't watch any of the scenes from their last night onwards on their own, only when I'm watching the whole film (not sure why, it just doesn't feel right watching any of it out of context
) so my memory of the scene where Jack's dad talks about Jack and Randall moving to LF is a bit sketchy, but I'm sure he says something like "he's got some other guy..." not "he asked some other guy..." or "he wanted some other guy..."
I've always felt that it was Randall's idea for him and Jack to move somewhere together, after all, it was Randall who made the first move on Jack in the first place, ok Jack did nothing to discourage him, but it's pretty clear (imo) that Randall was more into Jack than vice-versa. I'm not saying it didn't become more than just sex at some point,I'm sure Jack must have grown to have some sort of affection for him, but I can't see it being much more than just affection, because emotionally he didn't have anything more to give Randall,any love he had to give was for Ennis, so I don't think sharing the rest of his life with Randall would've occured to Jack, because that place in his dream was reserved for Ennis.
Randall, on the other hand (unless he had an "Ennis" himself, but assuming he didn't), could have easily fallen in love with Jack (well, haven't we all?
) and had the same idyllic fantasy about him and Jack living together. Jack could've talked to him about his parents' ranch,(presumably that's where he told Randall he was going when he went to be with Ennis), how it was in a bad way, etc, and Randall, being a ranch foreman himself, could've seen it a possibility for their future together and tried to sell the idea to Jack before that last meeting with Ennis. I think Jack would've rejected the idea at first, then after the argument with Ennis,angry and tired and broken as he was,thought it might be better to take what was on offer than waste anymore time waiting for something he was never going to get.
I know I'm really stubborn where this subject is concerned, I just can't accept that Jack was ever serious about living with Randall(at least not without telling Ennis about it first), so maybe that stubborness is clouding my thinking (such as it is
) here, but it makes more sense to me for Randall to be the one suggesting he and Jack live together.