What is the ruling on a person who after praying (Tasleem) blows on to his thumbs, wipes his eyes, and holds his head with right hand while saying something? Is there any authentic Hadith or support for this behavior?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

We do not know of any evidence in Sunnah or in the practice of the good ancestors proving the matter you mentioned in your question.  Therefore, one should give it up, for the Hadith of Ayisha (Radiya Allahu Anha) that the Prophet (Sallallahu Alaihi wa Sallam) said: "Whoever introduces in this faith of ours that which is not part of it, it is to be rejected" [Reported by Imams al-Bukhari and Muslim].

Allah knows best.