A full reading for Rat × Virgo meeting Goat × Gemini is on the way. In the meantime, the score above is computed from the canonical element matrix and sign-cycle distance, and the profiles below cover each side individually.
Both the blessing and the bane of members of this introverted DoubleSign is the capacity for complete disregard of all forms of outside impetus. Rat/Virgos have a private clock that tells you your own sweet time in which to do things, and you stick to it, regardless of the demanding voice, the wheedling phone call, or the looming deadline. Such independence can naturally lead to an unhealthy isolation in matters of the heart, and you should remember to make an effort now and then to ditch your Virgo half, have a night on the town and rub some elbows with the fast crowd once in a while.
The Goat/Gemini will talk a good game about "needing your space," but in reality you need people around you at all times, and not just any people, the right people -- that is, people who will provide input for your rapacious sense of ego. You need to feel connected, and any medium of communication will serve to dispel your sense of isolation -- phone, internet, even television are better than being left alone to listen to the hollow repetition of your own Gemini fears.