There could be a brake light switch issue. There could be a wiring or connector issue at the switch. Or there could be a completely different problem altogether - requiring hands on testing to determine the source of cruise control failure.
Use this link to find some shops near you that can help with your concern:
www.repairpal.com/repair-shops
RepairPal Certified shops can diagnose and repair your 2006 Chevrolet Avalanche 1500. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.