You cannot directly pair a generic wireless guitar (Bluetooth, proprietary 2.4 GHz dongle) to an Xbox 360. The console only recognizes its own Xbox 360 wireless protocol (used by official controllers and Guitar Hero/Rock Band guitars made specifically for 360).
Third-party adapters (e.g., CronusMAX, Titan One) can translate some controllers, but they're expensive, complex, and may violate Xbox Live terms.
Buy a wired Xbox 360 guitar (often $15–$30 used) or a wireless 360 guitar + dongle (ensure the dongle is included). Check "Xbox 360" on the box.