Like Major Gowen, Miss Tibbs and Miss Gatsby are not just guests at Fawlty Towers, they live there. Also like him, they are elderly and somewhat senile. They have apparently never been married, and so have no children to care for them.
Sweet old dears that they are, they fawn over Basil Fawlty, but he has as little use for them as he does any other guests at his hotel. He frequently makes snarky comments and cruel jokes about their old age to their faces, yet they seem not to notice. They even talk baby-talk to him and each other.
Miss Tibbs and Miss Gatsby always do everything together, except in 2x04 - The Kipper and the Corpse. In that episode, it is Miss Tibbs who sees Basil and Manuel dragging around the body of the unfortunate Mr. Leeman. Tibbs faints dead away and is left locked in a wardrobe with the corpse. When she wakes up, she is terrorized and nearly catatonic from fear.