It is traditionally believed that the Buddha was born, enlightened and passed away on the date(tithi) of Vesak. Now it does not seem to be very probable that all three major incidents of one's life would occur on the same date. What is the earliest source of this information about Vesak in the scripture?
You have to imagine whether you are in that time first, at the age of memorizing not reading like nowadays.
They almost always memorize all memories as approximation like we memorize as month, quarter, etc.
In pali, we called this kind of number as approximated number, Anekasankya. It's one of 5 types of number using in Pali canon, missa, gunita, sambandha, sanketa, aneka.
I have no idea for the birth date however it's make sense to say the enlightened month and the dead month are in the same month before VassaMasa (raining season) according to Tipitaka in VN Mahavagga Mahakhandhaka, VN Vassupanayikakhandhaka, VN Pañcasatikakkhandhaka, and DN MahaparinibbanaSutta.
It's make sense because in VN Mahavagga Mahakhandhaka and VN Vassupanayikakhandhaka the Buddha enlightened before walking from ๑(1) to ๒๐(20), see below picture, and lived his first raining season, 8th-11th month, at ๒๐(20).
And in VN Pañcasatikakkhandhaka, and DN MahaparinibbanaSutta, the Buddha was dead before raining season as well.
When we count the raining season, 8th, and walking timing together, it's make sense to be some date around 6th month, Visakha.
Reading without caring of tipitaka memorizer is ruining the readers' right view exactly.