Not sure if the answer is the same on an '01, but on my '04 Sierra I had the same problem. There is a big relay box under the hood on the driver's side mounted over the wheel well. There is a relay for the horn in there along with relays for many things you wouldn't think needed a relay. The layout is on the bottom of the big lid to the box. To check if it is the relay, swap it out with one of the other relays in the box. I have had to change 6 since I went over 200k. They are available at aftermarket parts stores for around $15.
The 2001 GMC Sierra-1500 has 12 valves.
The 2001 GMC Sierra-1500 has a V6 engine.
The 2001 GMC Sierra-2500HD has a V8 engine.
The 2001 GMC Sierra-2500HD has 16 valves.
The 2001 GMC Sierra-2500HD is a gas-powered vehicle.
The 2001 GMC Sierra-2500HD has overhead valves (OHV).
The 2001 GMC Sierra-1500 has overhead valves (OHV).
The 2001 GMC Sierra-1500 is a gas-powered vehicle.
The 2001 GMC Sierra-2500HD has a 5-speed manual.
The 2001 GMC Sierra-1500 has a 5-speed manual.
The height of the 2001 GMC Sierra-2500HD is 6 ft. 4.2 in. (76.2 in.).
The 2001 GMC Sierra-2500HD's turning circle is 43.8 ft..