F-Theory, as I understand it, is a realisation of Type IIB String Theory as a 12-dimensional theory in such a way that the $SL(2,\mathbb Z)$ symmetry becomes natural because Type IIB String Theory is F-Theory compactified on a torus.
Question 1: However, this explains only why F-Theory needs to be 12-dimensional. Why does one of these extra infinitesimal dimensions need to be temporal, though.
Question 2: I've also heard that F-Theory isn't exactly a 2-time theory. However, that doesn't make sense to me, as, since the metric signature needs to be $(-1,-1,1,1,1,1,1,1,1,1,1,1)$, i.e. mostly plus, with 2 temporals and 10 spatials. Or am I missing something obvious, here?