Rama explained his dilemma to discouraged Sugriva and encouraged Sugriva to seek another encounter with Vali.
This time Laxman uprooted a blossomed Gajapushpi creeper and tied it around the neck of Sugriva for identification.
The duel between Sugriva and Vali ensued for the second time (next day after the first duel) and this time Rama struck Vali with an arrow.
(pages 111-112 of The Historic Rama for details) that may refer to a solar eclipse.
Voyager 4.5 simulation for 22 September 12210 BCE shows early morning solar eclipse that was over by noon.
Valmiki Ramayana alludes to numerous astronomy references and analogies for this day. These are good examples of corroborative evidence. These, by themselves, individually or together, do not prove, do not establish, do not claim for the occurrence of solar eclipse on this day. However, if someone postulates (or proposes based on independent evidence) occurrence of solar eclipse on that day, such evidence provides supports for such conjecture (or a guess).
Corroboration is all we have. Corroboration only achieves what is described above. It does not prove anything. In fact we can not prove anything. We can only corroborate.
(1) Valmiki Ramayana compares Sugriva who was fighting with creeper (Gajapushpi) around his neck, second time around with the sun adorned with galaxy of stars in the sky.
(2) Vali, golden hue in color, was described as being rendered non-luminous like the eclipsed sun.
(3) The two fighting brothers, intent on finding vulnerable points of each other, resembled like the moon and the sun in the sky.
(4) Vali fell to the ground, and the earth appeared as dark as, the sky with the moon disappeared from it (Amawasya)
(5) After listening to the parting words of Vali, Sugriva felt wretched and appeared like a moon seized by Rahu.