That’s looking down the wrong end of the telescope, again, as in every time. Evolution has never stopped occurring, it is an intrinsic, inseparable property of life reproduction to the point of synonomy.
You are asserting that there [IS!] no evidence that ‘a character evolves slowly enough to have the same state in closely related taxa as opposed to varying randomly’, despite this for example.
Given that the fact of evolution and that the correlation of genes with the same expression in closely related taxa is axiomatic, where’s the fallacy?
Just Google ‘slowly evolving genes’ and expose any fallacy.