Crackpot theory incoming:

"Tsaesci" is also the name of the land of the Tsaesci, meaning "Snake palace". What if the snake-bodied Tsaesci are extinct? The men of Akavir found the ruins of their civilization (or were slaves who survived whatever killed the snakes) and took it over effectively becoming the Tsaesci culturally. Thus they were "eaten" by the Tsaesci culture.

however dont I recall a tsaesci advisor to someone who was literally described as snake-like?

As far as I remember there 'were' humans in Akavir, although they left. Though, Viigthor's theory is a very cool one, however dont I recall a tsaesci advisor to someone who was literally described as snake-like?

The only thing I recall is that Potentates Versidue-Shaie and Savirien-Chorak were described as snake-like, but the http://www.imperial-library.info/content/2920-last-year-first-era is to be taken with a grain of salt.

In the dawn of the year 320, a kinsman of Versidae-Shaie, Dinieras-Ves "the Iron", presented himself with a host of companions before the Potentate. It was he who suggested an order of mercantile warriors-for-hire, who could be hired by nobility in lieu of a standing army. The employment would be temporary, and a percentage of the fee would go to the Potentate's government, thus putting salve on two of Versidae-Shaie's greatest pains.

Though it was then called The Syffim, after the Tsaesci word for 'soldiers,' the organization that was to be known as the Fighters Guild had been born.

[...] When Akavir attacked Tamriel in the 2703rd year of the 1st era, they had been beaten back by the Reman Dynasty. Now they had a Potentate on the throne, and with Dinieras-Ves's machinations, the local armies would also be Akaviri. What they had failed to do by combat, they would have successfully accomplished by patience. A traditional strategem, many scholars suggest, of the immortal snake men, the Tsaesci of Akavir, who always had time on their side.

The point, however, is largely academic. Though the Syffim did establish themselves in some kingdoms neighboring Cyrodiil, it became quickly apparent that local warriors were needed. Part of the problem was simply that there were not enough Akaviri for the work that needed to be done. Another part was that the snake men did not understand the geography and politics of the regions they were assigned.