Why does my 2003 Silverado HD engine get hot when i'm backing up,even a small load on my trailer

Don't know where you came up with this - truck code showing is flash code 79 pcm ? That vehicle does not flash codes - you need to hook up a code reader or scan tool to view DTC'S - diagnostic trouble codes P0???

Chevy Silverado: Flashing Check Engine Light Diagnosis ' Drivetrain Resource (700r4transmissionhq.com)

GM vehicles 2003 to 2006 had stepper motor problems . Stepper motors control the instrument cluster gauge needles. Youtube videos - How to repair GM Instrument Cluster ' Speedometer ' Gauge ' Stepper - YouTube

you have a loose wire on the truck plug or a short

Mary, 2003 Chevrolet Silverado 2500HD suspension and steering diagrams. Check the attached links,instruction and guides, Good luck
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the braking system is not installed a the factory just the wire from the plug to the fire wall you need to add the fuse and control box

The wiring set up may not be the same on both trucks. Some people have their own way of wiring up trailers and its not matching the new truck

Maybe more info would be helpful, like gas, diesel, engine size, trans, cold, hot, morning first start,idle, driving down the road, accellerating?, coasting????????what you have checked and your results of those checks. Check eng light on? if so, codes?

mo me it sounds like low fuel volume i would check my lift pump

You need to replace your turn signal switch in the steering colum I just bought one from GM they are about 300.00

try changing the coolant temp sensor