I don't do it nowadays but WILL start doing it from this Avani Avittam.
Dear Shri Deviprasad,
Normally someone deciding to "commence" from the ensuing Avani avittam, is bound to leave it off sooner than later. So I suggest that you start doing it from the day you happen to see this post.
"sandhya" means the junction between day and night and if you will see the mantras (in the Brahmana texts) the case for Sandhyavandanam revolves on the belief that a group of asuras known as "mandeha" try - every morning and evening, without fail, ever since the Sun was created - to destroy his power; the "arghyam" given as part of the sandhyavandanam take the form of Vajra (of Indra) and destroys the asuras (mandehas) who perhaps get revived in the next 12 hours or so and come back again to attack Surya. The point I am making is, there is no mandeha attack at noon and there are ceratin classes within brahmins who are required to do sandhya only twice a day.
Incidentally, at the time of the upanayanam the boy (வடு) requests, "சாவித்திரியை உபதேசித்தருள வேண்டும்" (सावित्रीम् भो अनुब्रूहि) and the entire upanayanam centres around chanting (reciting) gayatri (savitri) only. The related sandhya procedures do not find a place in the upanayanam per se. Manu smriti also says:
ऋषयॊ दीर्घसन्ध्यत्वाद् दीर्घम् आयुर् अवाप्नुयुः । प्रज्ञाम् यशश्च कीर्तिम् च ब्रह्मवर्चसम् एव च॥४-९४
4.94. By prolonging the twilight devotions, the sages obtained long life, wisdom, honour, fame, and brahma tejas. Here also mention is only about Sandhya, not midday.
How and when the ancillary rituals of Sandhya started etc., are not clear, but there is a strong case for Sandhya being originally twice a day.
Also I don't think incidents in puranas refer to maadhyaahnikam done by any Rishi.
Learned members may please clarify.