Although it seems unlikely, I've made very good butt joints with 1/16" balsa by using thin CA. I cut the ends to be joined on an angle to avoid a stress riser, pressed them firmly (but not hard) together, taping along the seam, and flipped the assembly tape-side-down against my wax-papered table surface. I light-sanded across the seam (keeping it beneath the sanding block/bar) and then dragged the fine CA applicator (blood pipet) along the seam. The CA permeated the immediate area without puddling on the surface, but a quick swipe with a paper towel seemed a good precaution. The seam usually set immediately ('can use accelerant), allowing an immediate light sanding across the seam, which did not take just the balsa down along the seam, as might be expected. One fuselage like this was covered in doped glass cloth and never revealed the line. Two others covered with epoxied fiberglass and naturally did not reveal the line. My original P-Force kit fuselage, with it's thicker, joined, fore and aft sides, was also assembled this way and covered with lousy modern silkspan, but it's seams never showed over several years.
Here's one of the profile-fuselage sheeting joints. I'm sorry that I don't have a photo that reveals the smooth surface well, but you can see the arrangement. Mike Alimov showed me this method years ago, and it has always worked - no visible seams after finishing, despite mismatched wood.