The argument that a fat saint must be eating secretly at night, although he does not eat during the day and claims not to eat at all, is based on which means of knowledge as per classical Indian logic?

The reasoning is postulation, Arthapatti.

Two facts are accepted, that the saint is fat and that he does not eat during the day.

Being fat cannot be reconciled with not eating at all.

To make these facts consistent, secret eating at night is posited.

Assuming an unstated fact to remove such an inconsistency is the mark of Arthapatti.