I'd say its a combination of it all. The base concept is that of a soul. However a soul needs a living body to host it, in Belial at least. That's why avatars need organic cores. The Great Demons are the only creatures without this limitation. Its also the reason why classic inanimate TFs don't work, stone, rubber and other dead materials are unfit to host a soul, as much as they are unfit to keep body functions working in any possible way, excluding highly complex robots maybe that do not exit in Belial anyway (however, organic bodies could be altered to the point where they'd be almost indistinguishable from their dead or inorganic counterparts).

In case of extreme forms like living dildos and such, there would still be at least a form of nerve-cluster left, to take over the functions of the brain. Even if physically too small, with some mana-assistance and magical rewiring, it'd do the trick. Like the "living-from-mana" effect, it'd be more of a natural phenomena happening automatically, rather than a deliberate thing, although a demon or alchemist might be able to deliberately make alterations to it, if they wish to.