Is "monotonous" ever used as a synonym for "monotonic" in math? I saw a few questions and answers recently that wrote "monotonous" instead of "monotonic." Then I Googled and see a ton of usages of "monotonous" in M.SE instead of monotonic. It occurred to me this might be a locale issue. Are there any locales that actually use "monotonous" for "monotonic" in English-language mathematics, or is this always wrong?

It is always wrong. It is a clear error, which a native English-speaking mathematician would never commit.