I have now analysed the fragments of Timaeus, as collected by Karl Mueller in ‘Fragmenta Historicorum Graecorum’, Paris 1841.
There are 160 fragments of which a bare 11 contain chronological data. These are (using Mueller’s numbering):-
1. 21. Dionysius of Halikarnassos. Roman Antiquities .I 74
The foundation of Rome and Carthage is dated to 38 years before the first Olympiad. [814 BC]
2. 21a Syncellus Chron. P155 in Corpus Script. Byz. Vol VII
Rome was founded about the first Olympiad. [c.776 BC]
3. 40. Skymn. Of Chios description of the World v208ff
Massalia founded 120 years before the battle of Salamis. [599BC]
4. 47 Plutarch. Life of Lykourgos. 31
Lykourgos not much later than Homer.
5. 53. Schol. ap Appollonios of Rhodes. IV 1216
Chersikrates expelled Bacchiades from Korinth 600 years after the Trojan War. [603BC beginning of war or 593BC to end of war]
6. 91a Schol ap Pindar Ol V 19
Kamarina was refounded by Gelon in the 79th Olympiad. [460-56BC]
7. 92. Clement of Alexandra, Stromateis p355 Oxon
Xenophanes of Colophon lived at the time of Hiero and the poet Epicharmis, Apollodoros says he was born in the 40th (616-12BC) Olympiad and lived until the era of Darius and Cyrus.
8. 93. Diogesnes Laertius VIII 51 v ‘Empedokles’
Timaeus also reports that Empedokles was the son of Meton of Agrigentum...Eratosthenes says that Meton was alive in the 71st Olympiad.(492-488BC)
9. 119 Plutarch VIII Sympos. Quaest i
Euripides was born on the same day as the battle of Salamis and dies when Dionysius the Elder took power.
10. 148 Clement of Alexandria
Gave 820 years from Return of the Heraklidai to Alexander’s expedition [Return 1153BC]
11. 152 Censorinus On Birthdays 21
Gave 417 years between Fall of Troy and first Olympic Games. [Fall of Troy 1193BC]
So two events dated by Olympiad (foundations of Kamarina, Carthage and Rome{twice}) but no more specific than the four year range in the case of Kamarina; and it must be noted that the dates for Rome are in one case inaccurate, c.776 and in the other the source criticises his date. So much for the glowing reputation of Timaios’ work on the Olympic victors; in two cases it is other authors who give the Olympiad dating (Empedokles, where Timaios is adduced to support his patronage and citizenship not his dates and Xenophanes where Timaios only gave a context not a date). Likewise Lykourgos gets only a vague context and three further events are dated by the myths of Troy. Leaving one dated by a historical event, Salamis and the other, the lifespan of Euripides, seemingly tied to two specific days; and one of them a birthday! The problem is, that aside from no specific date being given, the purpose of the conjunctions seems to be the opportunity for a witticism, that the author of tragedy was born on an occasion of rejoicing and died on the day that the cause of so much tragedy came to power; the opposition of author and actor doesn’t quite work in Modern English (no, this is not evidence for Timaios’ lame sense of humour).
What is demonstrated is that more than nine out of ten cats preferred to reference his ethnology, history or geography than his chronology and that none of the references we have give a month, let alone a day. Maybe someone will insist that Timaios’ mention of Euripides lifespan indicates a lifelong interest in birthdays and that the accompanying play on words is a link to the ‘apt remark’ of Cicero and the ‘frigid’ one of Plutarch....there be the air, go build your castles. I’m staying on terra firma.

When you think about, it free-choice is the only possible option.