The most common reason for a simultaneous appearance of both the ABS and brake light on the dashboard of a 1999 Chevrolet Silverado is a faulty Electronic Brake Control Module, or EBCM. Scanning the vehicle's computer system will reveal a definitive error code, which should read C0265 for EBCM issues.
If a new module is not easily located or is too expensive, there are certain services, such as ModuleMaster, that rebuilds the faulty module for a cheaper cost.
Because the module is located in an area that is not easily accessible, professional help from an experienced mechanic may be required. The removal and re-installation requires a small torx bit head.