You can solder a small lead onto the cut portion and connect that to the factory harness. Your new LED 16' should indicate where you can safely cut and connect the leads. I'd also use clear shrink wrap and a little silicone over the new lead to keep moisture out of them. Good luck.
2019 Keystone Montana 3560RL
Truck: 2020 Chevy Silverado 2500 HD Duramax: Firestone airbags & Air Lift wireless compressor, Curt gooseneck, Anderson hitch, TST-507, Micro-Air thermostats & easy start. USMC combat vet & retired LEO. Robert, Anika, Breanna, Dylan & our dog Layla