Thank you so much for the information on casuality!
A 5-dimensional metric would just be dx^2 + dy^2 + dz^2 - dt^2 - dw^2 (where w is the other time-like coordinate.) A positive distance is still space like and a negative distance timelike.
I don’t dispute what you have said, but wonder how it relates to brane theory, which is where I see the conventional time dimension rendered as a plane rather than a line and hence the cause-effect muddling. In the linked article, the authors immediately proceed down the compactification path though I do not believe this is necessary and I really hadn’t considered how you would approach the eigen decomposition for 5D with 2 time dimensions or how you would figure a Minkowski metric with an extra dimension.
Still, the predicted consequences aren't so far observed.
Naturally, I’m not in the business of making predictions (and who would take me seriously anyway?) But of a truth, I would not be surprised to see an extra time dimension prediction involving a cosmological constant, especially with regard to dark energy. Strangely, everytime I get into researching brane theory I keep coming back to the University of Pennsylvania ala Physicist, Tegmark, Ovrut and now Tianjun Li on a Time-Like Extra Dimension and Cosmological Constant in Brane Models
I haven’t completely waded through that article yet, but so far it sounds like it is heading in the direction I was pondering concerning dark energy. Hmmmm….