According to most of the articles listed for Tut 3 at Google the figure around 1479 to 1425 BC seems to be the most accepted, with the first 20 to 22 years as a co-regency with Queen Hatshepsut. He was 2 when his father died. I am not familiar with Rohl’s chronology, nor have I heard about anyone proposed the reign end in the 12thc. I have heard of Manetho’s chronology, and work by Brestead (which I will have to wait to study as it is past my bedtime).
https://en.wikipedia.org/wiki/Thutmose_III
This link shows some of the complexities involved in sources and dating. https://www.ancientegyptonline.co.uk/manetho.html
Those most accepted figures are wrong by centuries. Hatshepsut was the Queen of Sheba, she syncs with King Solomon via an inscription she had made about her expedition to Punt, shows KS's port official and gives the name, which matches up with that of his son, who succeeded him in the job according to the OT.
The complexities in dating result from the preconceived notions about what the chronology "must be", and by complexities is meant, the conventional pseudochronology can't work, and therefore doesn't. I think a lot of people believe artifacts are dug up and found to have date stamps on them.