The most interesting answer is the deity that would become the Horned Rat.
Crack-Theory Time!
I think Solden, currently God of Tyranny and Oppression is actually a good fit for a proto-Horned Rat:
" Solden worshipers are organized into independent cells, each of which submits to the absolute authority of a single leader, and their meetings always involve the humiliation and denigration of one of their members"
Imagine an ascendant God of Tyranny, constructing a grand tower to place himself as Tyrant of the Southern Pantheon, and then the stranger comes and offers a deal that the Tyrants of Tylos cannot refuse, for a new god would surely just be subservient to Solden once Solden is Tyrant of even the other Gods.
Then the bell rings and Solden is cast out from the southern pantheon and his peoples are cast out from humanity and cursed, turned to rats.
The Grey Seers are the Priests and Tyrants of Solden who served directly for their horned tyrant.
The rest are cursed to be Skaven, endlessly fighting themselves and eachother for domination and tyranny over their individual cells.
Over thousands of years Great Clans finally rise with specific styles of Tyranny and Oppression that all serve the Horned Rat's Tyranny and submit to the Council's Will.
A tyranny of technology. A tyranny of shadows. A tyranny of flesh-made-coin.
A tyranny of zealous fervor. A tyranny of Militant Order.
He fits as a Southern God, of the trappings of civilization and bureaucracy and early organized rule.
Tilea, those that escaped Tylos, would come to hate Tyranny with a passion. They would likely form a culture described as:
"the Tileans are independent minded, strongly-willed, and some would say, impossible to govern by force"
the Estalians, migrants from Tylos that claimed abandoned elf colonies, may have changed less and emigrated sooner. They have a strong culture of Dueling, and if one is the strongest at swordplay one could become a Tyrant by carving all opposing claimants to ribbons. There is less flavor known of Estalians than of Tileans, so I cannot "crack-theory" further.
but yeah. That's my crack theory. Solden was a human god of Tyranny and reached for becoming Tyranny and Oppression so that he would have undisputed rule of all the Southern pantheon. Wishing to subjugate his fellow deities.
Something went wrong, and instead he became the Horned Rat, the undisputed ruler of corrupt and cowardly rats and nothing else.
there are still some very old and small human cults to the human face of Solden, but his primary worship base is now the Skaven and he hates it.
A Tyrant yes, with a following of those that only worship him, but the individual tyranny and oppression backstabbing and
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Myrmidia is missing from the coinage. The deified founders of Tilea are missing from the coinage. Other than that it could be just about anything. Proto-Horned-Rat is most interesting, with or without it being Solden
