I have a newer fwc. I went out and tested my Blue Sea 12v acc. Worked and held fine. I added 2 more for convenience. They can be purchased separately https://www.bluesea.com/products/1011/12_Volt_Dash_Socket
I wonder if a Lithium battery wouldn't solve this problem. Not a cheap solution, but they maintain almost full voltage until it drops off to almost zero.
Has anyone tried this https://navtv.com/products/NTV-KIT924/trailer-cam-view-tcv-ford3.html on their Ford F150?
The video shows a simple install, and override when the trailer/camper camera is installed.