this is just an observation with a slight derivation of possible answers I wish to share with you, I'm not sure if this has been posted before but as far as I can see it's not.
obviously in chapter 605 obito displayed his first use of "transparency" tech. it's the one where he uses the space time technique kamui from his MS to send bodyparts that overlap with the enemy or their attacks to the alternate dimension.
now I think in the recent chapter 606 a major clue of how it works has been revealed to us.
on page 2 of this chapter we clearly see him in tears stepping through kakashi, but he doesn't really have eye for kakashi since he is focused on Rin.
on the next page obito reaches out to Rin to try to grab her but again he passes through her on his first try. notice that all this time obito's MS is showing. and also obito is startled and surprised of passing through Rin.
later on he tries again to touch her and he really focuses on this and this time he does manage to grab her and pick her up.
this little sequence of actions and reactions makes me believe that his "transparency" tech is on as soon as he activates his MS, it happens without him having to make a decision about it or without it costing him a noticable amount of chakra. but he is capable of making the choice to keep his body parts in this dimension and be able to touch something.
from previous chapters in the fight with naruto and his fight with minato I guess we can also claim that as soon as a little part of his body is in the other dimension he can not chose to become all solid (the time he tried to grab naruto but guy stuck his foot trough obito gave me that thought, he was unable to touch naruto because a part of his body was in the other dimension chapter 566 pages 12 and 13)
the time limit that konan mentioned will also be true, I guess that is a limitation of the tech itself, a weakness sort of speak.
and it also makes for a big difference between kakashi's kamui and obito's kamui, kakashi has to chose when to activate it, obito has to chose when to deactivate it.
your thoughts are welcome