Is (으)시 sometimes used just to disambiguate between the first and
second person?
No. It is an honorific form. For example, '있다' could have two honorific forms, '계시다' and '있으시다'. The main difference is '계시다' is used when '있다' is a verb which means:
People's actions or state continue without changing: '그는 앉아 계시다. (He is sitting)'
People's actions or state have just finished and they remain so continuously: '그는 깨어 계시다. (He is now staying awake, He's just waken up
and is awake)'
'있으시다' is used when '있다' is an adjective. In other words, it is not honorific for any action or state explained above and it is very awkward to use '계시다' in place of '있으시다'. For example:
삼촌은 형님이 있으시다 (계시다 X). My uncle has an elder brother.
이어서 회장님의 말씀이 있으시겠습니다 (계시겠습니다 X). Subsequently, the chairman of the board will speak.
It is extremely difficult to tell between '계시다' and '있으시다' and the following link explains it well.
‘있다’에는 동사와 형용사 두 가지 쓰임이 있는데, 동사로 사용될 때는 높임말이 ‘계시다’가 되지만 형용사로 쓰일 때는
‘있으시다’를 써야 한다. 동사와 형용사는 활용형의 차이로 구분한다. 동사 ‘있다’는 ‘있어라/있자’처럼 명령형이나 청유형
어미와 자유롭게 결합하지만, 형용사일 때는 그런 어미와 어울리지 못한다.
[한국일보 "(우리말 톺아보기) 있으시다, 계시다"]