Thanks for reaching out! Your wiring should be pretty straight forward. You'll move your MV (Master Valve) wire to your M terminal in your Rachio. Your COM (common) will go in your common port, and then your zones will go in order 1-12. Your Aux may be just like you said, acting like a 13th zone. The Aux was designed to bypass your rain sensor so if you have any zones that cannot be skipped, it will run even with the sensor activated. This will act as a normal zone.
You won't need to use any of the wires in your upper left corner (24VAC, SENS, GND), those provide power to your RainBird controller and sensor. Since your sensor is defunct, you're all set to not move those wires over. If you decide to get a rain sensor, let us know and we can help with your wiring!
Let me know if you have any questions and I'll be happy to help!
Have a great night,