The only way to make an "elective" faction AFAIK is to use the FN_GERMAN_HRE faction label for that faction. You can also use the Viking faction from VI. I can't remember which number they are but it's FN_(faction no.) rather than FN_(faction name). Though if non christian they are also prone to being converted to christianity once their provinces are converted. The only other faction is the FN_PAPAL, but this faction has even more hardcoded restrictions built around it which means it's best avoided.
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