Whoa there cowboy! The gas gauge has a voltage input terminal and a sender input terminal. If you read the TIP SECTION under "12V conversion" you will see a GMC tip at top, then the 12V conversion next. Read them both and you will have all the info you need.
Neither of the gauge terminals are grounded. The sender is grounded by it's mounting screws to tank (and a backup wire) and the gauge is grounded by the case touching the panel. As far as which gauge terminal is hot and which is sender, other AD GMC owners will have to tell you. You may burn it out by wrong wiring I believe. I see a red wire which is usually hot and brown wire is usually sender.
But needs confirmed. Because this says differently. If this is your tag....and if the tag is on the correct terminal. Let a
GMC guy tell you what the "E" side terminal is and what the "F" side terminal is. Don't go by passenger side and driver side...... or left and right when conversing.