yati is a line-internal rhyme pattern, while prāsa is line-external.” (-Indira Peterson).

This is not correct as far as Tamil is concerned. The second syllable rhyme can also occur within a line in different patterns. Assuming there are are four feet in a line, the second-syllable rhyming can occur in different patterns such as between feet 1 and 2; 1 and 3; 1 and 4; 1, 2, and 3; 1, 3, and 4; 1, 2, and 4; and 1, 2, 3, and 4.

Even in Telugu, there is a 'line-integral' (intra-line?) second syllable rhyming. But that is an optional provision as alternative to first syllable rhyming called ' akshara maitri in yati' or just 'yati'. The optional provision of second syllable rhyming as alternative to first syllable rhyming is called 'prAsayati'. 

This provision is only for native Telugu meters (meters not borrowed from Sankrit or Prakrit). In the description of Prof. Sudalaimuthu Palaniappan for Tamil, the rule for this is in terms of the order of the foot (first, second etc.) within a line unlike in the case of Sanskrit borrowed meters where the rule is in terms of  the order of the syllable within a line. This provision applies to Geyams (मात्राच्छंदस्) and Telugu songs of Carnatic Music too. 

Thus it may be seen that inter-line second syllable rhyming is a nitya (inescapable) rule for Sanskrit-borrowed meters, the intra-line second syllable rhyme is an optional provision for the native Telugu meters.