Does the Hebrew in this passage specify is Saul was doing #1 or #2, or does it use a generic, non-specific term for “relieving himself”?
It’s not just you, and it’s not just the translation you’re using. The actual Hebrew uses a relatively obscure phrase, which is why many of the classical commentators go out of their way to explain it. Literally, it translates as “Saul went in to cover his legs”. The commentators [Rashi, Radak, Ralbag] explain that this is a euphemism for defecating.