In those cases the transitive nature of the verb's use is deciding. For instance, if I use "geritten" (rode, as in "rode a horse") intransitive ("Ich bin als junger Mann jeden Tag geritten.") then the auxiliary verb to use is "sein". On the other hand, if I use "geritten" transitive ("Ich habe noch nie eine Kamel geritten."), then the auxiliary verb being used is "haben".
HTH
Armin