In most families , the first tonsure of the child will be done before the family diety. we are also tanjore vadama brahmin . My family kula deivam is aerikarai mariamman which is in terilandoor where kamban got kali arul to write kamba ramayanam in tamil. For my children, first i went there for tonsure and then to thirupathy venkatachalapathy temple.
THis can be done before the completion of the first year itself or immediately after. In some families , this will be done in odd no. of years, first, third, fifth year. The baby will be gifted with a new dress for the occassion. As this being a vow on completion of the ceremony samaradhanai will be done.
As per the hair growth condition of your grand son you can do before or after the completion of one year. If your kula deivam is thirupathy venkatachalapathy you can go there for first headshave.
Good stars for tonsure are : aswathy, Rohini, Mirugaserusham, punapoosam,poosam, uthiram, anusham, chithirai, swathy, uthradam, thiruvonam, avittam, sadayam, uthiratadhi and revathy.
Good thithis are: dwithiyai; thruthiyai, panchami,sapthami, dasami, thrayodasi.
Good lagnams: rishabam, mithunam,kadagam, kanni, thulam, dhanus and meenam.
The eighth rasi from lagnam must be empty without any planets.
Do not do on the 3rd, 5 th and the 7th stars from the birth star of your grand son. wish you all the best.