The fuel pump on my 97 Chevy Silverado stays on after I turn the ignition off
The solenoid is stuck in the "on" position and will eventually burn itself out. Get it to a repair shop and have them swap out the part of the assembly. You can even pull one from a junk yard and bring it in to them if you aren't comfortable changing it yourself. Best of luck.
That controls the on/off functions of the fuel pump. I have a 98 GMC Sierra Z71 with 58k original miles on it (it was my grandpa's rig) and I use it to tow my airstream. This same issue happened. The solenoid stuck on, and burned out the fuel pump in just a few months after I ignored it. Its like a $15 part if you pull it yourself.
Looking for a Used C/K 1500 in your area?
CarGurus has 906 nationwide C/K 1500 listings starting at $2,500.
Search Chevrolet C/K 1500 Questions
Chevrolet C/K 1500 Experts