Tailgate support rack

Building a support like that is easy enough with some minimal/moderate fab skills and tools.
Couple considerations:
1. Are you sure the tailgate is "flat" with the truck bed? and if not, can you lower it enough to clear the camper without it resting on the bumper?
2. Bigger consideration, finding a way to support/attach to the tailgate that a. Keeps the tailgate form bouncing. and b. doesn't damage the tailgate.
3. Does it have one of those ladders and can you use that as one leg of the support? Resolves any issue of attaching on or around the Sheetmetal surface of the tailgate.

Possible ideas
1. Assuming the tailgate is on the same plane as the truck bed or truck bed built up enough to clear higher tailgate surface. How much in conflict is it fore/aft with the cables? Can you move the camper back just a couple/few inches and clear the factory cables? IMO this would be ideal unless your load is that critical weight wise that moving it back a bit is a weight issue (not likely, but someone who OCDs on center of gravity will point that out)
2. Can you build dummy hooks lower on the tailgate (closer to the truck bed) to clear the camper and still allow enough angle to support just the dead weight of the tailgate? The mounts on the tailgate would have to clear the truck bed when closed.
3. A combo of 1 and 2.
4. A "must" for a tailgate is keeping things from departing the truck bed when you don't want them to. A luxury is the backup camera which you likely have and is likely tailgate mounted. You can get another OE camera and mount it elsewhere if that is a "must" and you can simply use a board in the divider pockets near the rear of the bed for a simple fixed tailgate to keep items from sliding out.

The last idea is what we did for years. I used to just leave the tailgate on, until I built a generator rack in one back corner that conflicted with the tailgate cable. Doing the same as you, needing something to keep items in the bed when running around bobtail with no tailgate, I had a 2x10 that I slid into the bed pockets and when the camper was on, stored it next to the camper between the camper and wheelwell. (It also made a nice ad hoc guide for getting the camper loaded up, centered.)

I would leave the end gate at home and buy the cargo net for the truck box.

I'd also leave it at home and use a removable net.

I agree with Old Days and jim. Even if the tailgate is "flat" it probably will bear more weight than designed to handle.

^Which, like using a board in the bed pockets is a cheap simple reliable no frills solution.
I’d say the board is the cheapest option, but with the price of lumber….lol

Are you sure you can lower the gate enough yet not crease it against the bumper? Like others, I would leave it off the truck.

Old Days wrote:
I would leave the end gate at home and buy the cargo net for the truck box.

X2 on this.

BurbMan wrote:

Old Days wrote:
I would leave the end gate at home and buy the cargo net for the truck box.

X2 on this.

X3 leave the tailgate off the truck when the camper is on the truck.

Many decades ago, I ran my '69 El Camino for a couple thousand miles with tailgate open. Road grime and stuff pretty much ruined the paint on outside of gate.