I've been pondering on this for some time - at one time I thought the suffix might be '-mach', but a) I can't remember why and b) I recall deciding that'd be wrong.

I know of no suffix -mach in English or Classical Greek. Some words end in -mach, as in in stomach (from Greek, via Latin, στομαχος (stomakhos) 'gullet' fr. στομα (stoma) 'mouth', you can see that the m belongs to the original word/root, and that -akhos is some kind of diminutive suffix), and there are some words that are compounds from Greek that come from an original makhē 'battle' (e.g., theomachy 'war of the gods' fr. Gk θεομαχια (theomakhia)).

Ceci n'est pas un seing.