The shift solenoid on a 1998 Chevy Silverado is
inside the transmission. There isn't a single, easily accessible shift solenoid; the 4L60E transmission (most common in that year) has several solenoids. They're not externally located but are inside the valve body, which is a part of the transmission itself. To access them, you'll need to remove the transmission.
Therefore, you won't find it under the hood or easily accessible anywhere externally. Any repair or replacement requires transmission removal and disassembly by a qualified mechanic.
