I took two needles and thread and let's go!
You can see my original pattern. I sewed the sides laid flat as long as possible. The stitch is noticeable only at the wrong side. How did I do that?
As the leather doesn't fray, you can sew very close to the edge. The trick is that the needle goes in the leather through the side and comes out at the top (and vice versa). It took me quite a lot of time since I've seen this stitch to believe it really works and is safe:-D
When I could no longer sew it flat, I finished one seam and than the other. I secured the ends with about three stitches at the same place.
Unfortunately, I managed to lose my new thimble before I could took the final photo. I looks somewhat like Ronald Rich's one, who was my original inspiration :-)
But I loved how it fitted and if I don't find it, I'll be sure to make a new one.