what sort of evidence is being held out for the existence of a TEMPORAL QUANTA?

Answer 1

The idea for quantum time emerges from the ability to combine the speed of light, the Universal gravitatonal constant, and Planck's constant to derive something of an absolute time. The manipulation of these constants yield a time of roughly 10^-43 s, which has been named Planck time. However, I don't think that this has been shown to have any pratical applications as of yet.

Answer 2

Not much. There seems to be much more evidence for the concepts of a-temporality and dynamic equilibrium.