On a brand new 2008 Silverado I bought, it did not come with the fuse that energizes the 7 pin charge circuit. Look in the owners manual to see what position the fuse goes in and see if it's there. Also, the Silverado charge pin is only energized with the tow/haul button on or (I believe) the lights full on.
Here is some info on a later model Silverado. If I remember correctly, the wire wasn't even connected at the fuse box either:
https://www.silveradosierra.com/elec...10.html#p36107