"It's not just about the captain", was and is valid in other formats. But IPL, with non-playing leader a possibility, it's the attitude that harbors security that takes your team forward.
It is true for all forms of cricket that captain's attitude and belief in his 'core' player is important. In situations other than in franchise cricket, you can't keep on sticking with your 'core' group because say at a national level you have a wider pool of talent you get to choose and replenish the 'core' from. But in IPL (franchise cricket), you have a small pool that can't change till next season and your 'core' already has the best possible players for the current season. So stick with the core - always : this is the mantra the Shane Warne used to great effect in IPL1.
Mind games have no place in T20, being clear in the head about your place in a team/situation brings about clarity in execution and that is vital because you don't get that much time to correct your mistakes.
This is what some do wrong - continuing in 'political' captaincy, which is to not have good communication among all involved. So that the sole source of information (hence authority) is the captain. T20 doesn't have place for such captains.
Physiologically (which governs the physical aspect right away), we respond quicker to feeling than to thought. But thought follows soon after and if even the first few second of the thought are in line with what was felt, we no longer 'think' but start to 'act' positively and without 'second thoughts'.
Great captain inspires in his boys a feeling that they should win. But when lines of communication are sometimes not great and roles not well defined (which happens when the leader is insecure) - that feeling for winning is not in line with the 'thought' of how to clearly go about it. When a captain fails in IPL he is more insecure because its a private enterprise which invested millions into it. This causes more confusion as to what one's role is and also who defines it - is it the under performing captain? is it the coach? is it that owner who holds the purse strings? No one knows where to look, what to do or even if their role in next game will be a playing one.
In a leaderless everyone is a 'hero' scenario, you don't look to define your roles but you just 'go for it'. This was how many teams were in first two IPL's. So the game was often won by one or two performances. But to be a 'hero' every game is not easy. And by being a 'hero' in one game - you win your team that game, but also to certain extent you affect the morale of other "hero's" who failed to perform. As one can't be a 'hero' every game you need to almost find a new 'hero' every game or two - which is difficult. This what 'form' is - a expression of confidence based on prior performances - but sooner that later (sooner in T20) you fall out of form - by that time the other "hero's" of your team are low in confidence - they are 'not in form'.
It was easier for Warne to stick to a core and not be bothered about his own 'form' in IPL-1 because he was a giant among the unknowns of RR back then. In essence he never had to sit out for lack of performance. But for a captain who is one among the core group - for one like Gambhir this IPL, its vital that he sacrifices himself for the betterment of the team (not that Gambhir needs to do that, as he is doing better that other 'core' of KKR) if necessary.
It is also vital that the captain makes this position clear to his peers ('boys'):
1) we will stick with the 'core' no matter who performs
2) just by being captain, I have no confirmed berth
Hence the evolved captain's of IPL today, go for believing in the 'core' more than they believe in any individual, even their own selves. By doing this (they have come to understand) they aren't making their situation insecure - this is how the format is: Where a non-playing captain is still the leader.