What is the best time to perform Amavasya Tharpanam? Is there any specific reason why it should be done at that time ?
As per the Agastiar.org website sunrise and noon are the recommended times of the day to perform Pitru Tarpana.
When to do Tharpanam?
Sathguru Venkataraman said that according to Maha Guru Agasthiar, tharpanam should be done at sunrise. There is a tradition that says that tharpanam should be done at noon. If this is your tradition, please do follow that.
Is there any specific reason why it should be done at that time ?
As you can see no such reasons are specified.
As per the Katyayana Smriti noon is the best time.Evening is not recommended at all.
A Sraddha in which Pindas are to be offered for the gratification for a month, is to be preferably performed on the wane of the Moon (Amavasya-day) ; it should be performed in the third part of the day, but never towards the evening,.
Katyayana Smriti,Chapter 16