Sumathi asked me about the language connection between Tamil and Japanese. I don't have the related books with me right now, but as to the time of the origin, probably nobody can say for sure. The books I read were written by Oono Susumu, the most well known Japanese linguist, and his interviews conducted by Shiba Ryotaro, the best selling historical novelist in Japan. The following link I found is in English.
More detail below.