How to distribute function clauses over several files

Generally: just don’t, you can’t achieve it the way you aimed at for the reasons @Qqwy explained excellently.

But if you really want to have some sort of routing, you might be better off just making one central router module which just delegates to a number of other modules.

Protocols I would advise against; you can make do without them for sure.

Finally, you can use behaviours and runtime hackery to dispatch to a compliant one but IMO that’s an overkill as well.

IMO just go for a router module that dispatches function calls to other modules. Standardize those modules somehow. Easiest way would be to just clump them up in one directory but if you really want to be able to find them at runtime, you can also make them implement a behaviour.