Sagittarius on the inside, Gemini on the way in.
Your sun in Sagittarius (fire, mutable) is the engine — what burns at the centre, what adapts when you are at home in yourself. Your Gemini rising (air, mutable, ruled by Mercury) is the door — the way you arrive in a room, the first read the world takes of you, the body you walk in.
Strangers tend to assume you are witty and detached — that is the Gemini arriving first. Then they get to know you and discover the Sagittarius fire underneath, which can be a layered second read — they have to update their first impression.
Reads as Gemini until you trust them; then Sagittarius comes through. The mutable-mutable mix means you consistently adapts.