[Alamo-Girl]

Just to let you know - and for any Lurkers following - the point you both made that time dimensions must be odd, here is my first substantive find:

Why odd-space and odd-time dimensions in even dimensional spaces? (pdf)

I'm still pondering on this article and the significance with regard to brane theory. Thank y'all so much for this line of inquiry!!!

[Doctor Stochastic]

My extrapolation would be that there can only be 1,3,7, or maybe 15 time-like dimensions no matter the number of space-like dimensions. Of course, this is only an algebraic approach and need not be correct. The paper you noted looks at things from a different viewpoint.