There is indeed a principle behind the ordering of letters in Indian languages taken from Sanskrit, and AFAICT Tamil also follows it.

க் ங்
ச் ஞ்
ட் ண்
த் ந்
ப் ம்

If we look at it rowwise, the first row is the velar consonants, then the palatal then retroflex then dental then labial. If you notice here, we are gradually moving from the back of the mouth to the front!

If we look at it columnwise the first column consists of unvoiced/voiced consonants and the second column consists of nasals.

Then come the semivowels
ய் ர் ல் வ் ழ் ள்

After that 
ற் ன்


शनि, 2 जुल॰ 2022, 4:02 pm को Visuwesh <visuweshm@gmail.com> ने लिखा:
[சனி ஜூலை 02, 2022] Eli Zaretskii wrote:

>> > So, then please explain what should be the "correct" order within each
>> > sub-list.  Is the correct order within each sub-list in the ascending
>> > order of the codepoint?  If not, what is the correct order?
>> >
>>
>> The correct order is not the ascending order of the codepoint, the
>> correct order is
>>
>> க ங ச ஞ ட ண த ந ப ம ய ர ல வ ழ ள ற ன
>>
>> and their respective codepoints are
>>
>> 2965 2969 2970 2974 2975 2979 2980 2984 2986 2990 2991 2992 2994 2997 2996 2995 2993 2985
>
> Why is this the correct order?  Does it have any definition based on
> some principles, not just on the above list?

I'm not sure if there is a principle behind it.  Is there a principle
behind why a comes first after b?  Same thing, I suppose.  But it does
raise my brow when I see them out of order which is why I'm bothering to
sort them.