Dear Alistair, apologies for missing your question.
Gyan Mudra, also known as the "Mudra of Knowledge," is a hand gesture that is often used in meditation and pranayama practices. It is said to enhance concentration, focus, and mental clarity.
One similar mudra is Chin Mudra which is also called the "Mudra of Consciousness." It is formed by bringing the tip of the index finger to the base of the thumb, and is said to promote a sense of inner peace and tranquility.
If I assume that the thumb on the right side of index finger, then the mudra you are describing may be called Shuni Mudra, it is a hand gesture that is often used in meditation and pranayama practices. It is formed by touching the tip of the middle finger to the tip of the thumb, and the thumb is placed on the side of the index finger.
Shuni Mudra is said to be associated with the element of earth and is believed to promote patience, perseverance, and humility. It is also said to help in calming the mind and developing inner focus, and to balance the energy flow in the body. It is said to be useful for people who are prone to anger, frustration and impulsiveness.
Please tell me if I am wrong or could not get to you properly, so that I can explore & study further.