I think the biggest determiner of how the space would go is whether you feel it is desirable to have a shower/toilet in the cabin of the camper. Most who have a 13ft don't because the amount of real estate is so limited. If you want one inside determining if you want the facilities placed in the middle of the cabin to be secreted when not in use or if you want to dedicate footage on the perimeter also pushes the rest of the design.
My thought for a 13ft would be a cabin arrangement like one of Scamp's custom units. Check out Lorene W's 13ft unit.
Scamp custom photosSince you are building from scratch, I'd probably have a drainage hole in the middle of the floor to be used with a portable/removable shower unit. Ken James and several 13ft owners use shower curtains, tarps and etc as a shower curtain that they attach to the ceiling for a temporary water barrier when they shower. They use various types of contaners for drainage pans. I'd have a water catcher pan and I'd use the hole which a hose could be run through to route the drainage wherever desired. If the floor middle weren't resting on a truck bed, I'd look at reinforcing the Scamp bottom in the middle.
Portable Temporary Shower design:Ken James' UnitPopup Times ArchiveI've seen washing machine drain pans and hot water heater pans used for catch basins with portable showers. The advantage of those is they have a drain plug that a hose can attach to. So a drain hose could be run from your catch basin through the center drain hole and outside and away from the camper. If you are handy(saying this to a man who purchased a gutted trailer), adding a threaded drain plug to a plastic basin of your choosing is very doable.
Alternatively, outside arrangements work for some. I'm not sure how much remaining footprint you would have on your truck bed once you place the Scamp shell there. If there is space, you could have an outside shower like
Bivouac Buddy or use a privacy tent.