I think the inner life of the character, his ennui, his disdain, his attitudes, were always there from the very beginning. Indeed Bond's inner thoughts are what makes the books, to this day, always a more rewarding experience to come back to than the films. If anything, Bond's attitudes regarding the world around him are the primary focus of Fleming's writing, with action and plot in second place.
Of course it becomes more pronounced in the later books, but I don't think it's Bond growing dimensions, because anyone who's read Casino Royale knows he already had them -- it's about Fleming becoming tired of the series and wanting to try new things, working out his own frustrations as he grew older into the character who by the end of the series is very very tired of the game. Stories like The Living Daylights, and the OHMSS-YOLT-TMWTGG arc express a weariness, as Bond sees the world around him change and he's not too particularly fond of risking his neck for it anymore.
This is, of course, what so many of the continuation novels lacked. There's an arc to Fleming's Bond -- not a dramatically obvious one, but there's still a development: he's not the same fellow in that last book that he was in the first. And that's one of the (several) reasons Devil May Care was so off -- the older Bond of 1967 it supposed, three years after the events of TMWTGG, feels more like the Bond of MR or FRWL than the tired, bitter, resigned fortysomething he is by the end of Fleming's tenure.
Kingsley Amis captures the feel a bit better in Colonel Sun, but focuses more on the ancilliary characters than Bond, who is of course galvanised by the threat to M himself and also in his new unique relationship with Ariadne. Honestly I think Pearson hit the mark best of all for the feel of an "older" Bond in his Authorized Biography. Either way, only those two authors have ever approached replicating the feel of Bond's inner life.
The problem is, that this inner life, which as I said before is really the secret ingredient to the unique flavour of the novels, is really Fleming's inner life. His attitudes, his weariness, his bitterness. That's why it's never been replicated and never can be -- this inner character is why Fleming is Bond, not because Ian went galivanting around on OTT spy adventures like this Dominic Cooper TV series wants you to think.