The transfer case control module (also sometimes called the transfer case actuator or shift motor) on a 1999 Chevy Silverado is
located on the driver's side of the transmission, near the transfer case itself. It's not easily visible without some disassembly; you'll likely need to get under the truck to find it. It's usually attached to the side of the transfer case with bolts.
It's a small, electrically controlled unit. A picture of the specific module for your year and model Silverado would be helpful in pinpoint location, but a general location is as described above. Be aware that there might be slight variations depending on the specific transfer case type installed in your truck (NP246, NP263, etc.).
