What Sun does in a chart
Sun is the part of the chart that answers one question:Who am I when I feel most like myself? It describes core identity — not events, and not outcomes.
What Gemini does to it
Gemini is a air sign, so it moves on ideas and conversation. It is also mutable, which means it adapts things. Put those together with Sun and you get identity through curiosity — curious, verbal, restless, applied specifically to core identity.
Gemini is ruled by Mercury, so this placement tends to be coloured by thinking and talking as well.
The useful version
Placements are not verdicts. This one describes a default setting, not a limit — the things listed above are what you do when you are not thinking about it, which is exactly why noticing them is worth something.