For me the Constant basically enabled the mind to create some sort of relationship between the two time zones. It let Des create a sort of anchor (as you say Roc) in both the past and the present. Before this his concious mind was only able to focus on the past time zone, it could not make the connection between the two and therefore he didn't know anything that was going on in the present. Having a Constant, Penny, enabled him to recognise the present and give his conscious mind a way to recognise the two tenses, as Penny was in both of them. It is only by recognising the two time tenses that he's in that Desmond's conscious mind can establish itself. Eloise's and Minkowski's minds couldn't do this as they didn't have a Constant, an anchor that could help them establish their conscious mind in the present. Once your mind can establish itself in the present then it prevents itself from imploding ala Eloise and Minkowski.
Therefore once you have a Constant, the mind can stop switching as it has established itself.
That's how I see it anyway
