[jacobolus]

I have not seen any evidence that ancient Mesopotamians counted phalanges using their thumbs.

I believe that counting method was devised by some fan of duodecimal arithmetic sometime within the past century, and has nothing to do with sexagesimal numeration per se.

[garmaine]

It’s visually built into the cuneiform:

https://en.m.wikipedia.org/wiki/Babylonian_numerals

[jacobolus]

If that is your evidence then you are tricking yourself, or to be generous speculating wildly.

The evolution here was: physical clay counters; physical clay counters sealed in a clay envelope; physical clay counters sealed in a clay envelope but also pressed into the outside of the envelope to indicate how many; clay tablet with counters pressed into the outside (since the envelopes with counters inside were redundant); clay tablets with little cuneiform symbols to represent quantities, differing by type of object being counted, and not all sexagesimal; more uniform written sexagesimal writing system.

There is no indication in the symbols about how people counted on their fingers.