Ramayan refers to the solar eclipse at the time of war with Khar-Dushan in later half of 13th year of Shri Ram’s stay in the forests.
The story of Shri Ram‘s life was first narrated by Maharishi Valmiki in the ‘Ramayan’ which was written after Shri Ram was crowned as the king of Ayodhya, Maharishi Valmiki had a great sense of astronomy as he has made sequential astronomical references on important dates related to the life of Shri Ram indicating the location of planets vis-à-vis the zodiac constellations and other visible stars (nakshatras).
In Sunder Kaand there is a reference to lunar eclipse when Hanuman spots Sita in Ashok Vatika (5/19/14, 5/29/7, 5/35/87).
Sky view reveals lunar eclipse starting from 4.15 pm on 12th September 5076 BC from Colombo (7°N; 80°E) All these sequentially fully tally with the description in Ramayan.
Thus Shri Ram had come back to Ayodhya when he was 39 years old (5114-5075). Ram Autar, have researched on places visited by Shri Ram during 14 years of exile.
They sequentially moved to the places stated as visited by Shri Ram in the Valmiki Ramayan.