I'm looking for a word that refers to the state of being external or internal as a noun. Something like "ternality" or "ternalness" if those were words.
"The 'ternality' of the door was external."
If something is internal, it's obviously bounded by the limits of whatever it's contained within (a house, your body, etc.). If it's external it must be outside those limits (it's not bounded). So...
boundedness - the quality or state of being bounded (Merriam-Webster)
For an obviously "boolean" attribute like this, it's also perfectly natural to simply use a word identifying one of the two possible states. Just as we can refer to the truth of a statement (an "attribute" whose value can be either true or false), so we could refer to the...
internality - the quality or fact of being internal (in various senses) (OED)
...where the possible values of the boolean attribute are internal and external.
I read the great responses above. I thought about it and developed these two to explain both dimensions:
1. Inexternal, inexternality 2. Exinternal, exinternality.
These words are using "in" interior and "ex" exterior to describe both internal and external state/condition of being/object/response.