The writing on the pot is in Tamil Brahmi, a writing system that only fairly recently has come to be well understood. It says: n̪a:kan uɾal, Old Tamil for "Naakan's (pot with) toddy-sap". In modern Tamil writing this would be: நாகன் உறல்.
I think the Tamil should be நாகன் ஊறல் (nākaṉ ūṟal) - the article in The Hindu notes that the vowel should be long (romanized as oo):
The Tamil word ooRal (from ooRu ‘to ooze’) meaning ‘freshly tapped toddy’ is spelt here with the short vowel u probably due to oversight or reflecting the colloquial usage.
Tamil-Brāhmī was an intermediary between Brāhmī and Vaṭṭeḻuttu, which was used between the 5th and 6th centuries CE. The modern Tamil script is descended from Aśōkan Brāhmī - here is a comparison.
This site has a chart for Tamil-Brāhmī. It's very similar to Brāhmī but has letters for the alveolar sounds of Old Tamil. Out of interest, I made an image of what nākaṉ uṟal might look like in Tamil-Brāhmī. Of course I could be very wrong.
I see the second word, but I probably am wrong about the first word.
Another south Indian script that is not used much nowadays is Grantha, developed for writing Sanskrit. Here is a photo I took in Mamallapuram, Tamil Nadu, of what I think is a Pallava Grantha inscription.
And here's another photo... I think this is Vaṭṭeḻuttu.
Here's an article on early Tamil epigraphy.