Homophonic Substitution Cipher

A homophonic substitution cipher is a type of monoalphabetic substitution cipher which is a bit more secure than a simple substitution cipher due to having multiple copies of some (or all) letters in the alphabet, which are called homophones. Introducing these extra copies of letters allows the ciphertext alphabet size to be larger than the (source) plaintext alphabet size, and if the homophones are chosen roughly in proportion to the frequency of letters in natural language, it allows the frequency distribution to be masked, making frequency analysis less effective. Typically, letters in the original plaintext are replaced with possible homophones randomly, because this makes it the most difficult to solve. However, all homophonic substitutions have in common that if a particular ciphertext symbol is used somewhere, that symbol always corresponds to the same plaintext letter. There can just be multiple ciphertext letters that correspond to homophones of the same plaintext letter. This is why the method is still monoalphabetic, in contrast to polyalphabetic substitutions where the same ciphertext letter can mean different things in different contexts.

The eyes are not a homophonic substitution cipher (and not a monoalphabetic substitution cipher in general).

The largest piece of evidence we have for this is that if they were, tools like AZDecrypt would have been able to solve them fairly easily, and we would have been done with this puzzle in a week rather than the 5 years we've spent on it. Additionally, isomorphs are an observed property of the eyes which are strong evidence for them being polyalphabetic directly.