I will try automating and see what that does, but I think it will show up when I complete accelerated construction. If not, I found a thread that gives me a good idea what it needs to contain. Sadly, at third level tech, the max ship size is 400. That makes for a very small (and weak) resupply ship. I will probably wait until I can build size 500 ships before I invest.
Resupply Ships, Construction Ships, and Colony Ships use the Base Size Limit rather than the Ship Size Limit, if I recall correctly; I know they do in Shadows and Universe, and I don't think it was any different in Legends (though it's been a while since I played Legends, so I could be mistaken). I don't recall exactly what the Base Size Limit is at third level tech, but I rather suspect you might be able to build a larger Resupply Ship than you think.