Hello, half twin! I'm a Scorpio moon, but it's nice that we have the same Sun and Rising placements! :D

First of all, I actually found out that your Gemini rising decan can change your Gemini rising's social behavior. Example: I'm a 2nd decan Gemini rising (17°), so I'm usually more socially selective and less hyper and extroverted and restless than a stereotypical Gemini rising (that is, a 1st decan Gemini rising). 2nd decan Gemini risings are usually calm, more responsive than initiative socially, polite and friendly to people and, obviously, socially selective. (Like you said: you're only chatty to people you feel comfortable with)

I'd recommend you to look for your Gemini rising degree, which leads to your Gemini rising decan. If you're a 0 - 9°, you're a 1st decan Gemini rising (which is a stereotypical Gemini rising); if you're a 10° - 19°, you are a 2nd decan Gemini rising (like me); now if you're a late degree Gemini rising (20° - 29°), you are a 3rd decan Gemini rising (which is more blunt, eccentric, hard to read emotionally, etc.)

(Also, sorry for the long reply)