If you want to make a more casual vest, or you don't like the idea of the back being made from lining fabric, you can make your vest fully lined. This will also make it possible for your vest to be reversible.
To do this, simply cut one back piece from your main fabric and one from your lining fabric, the same as you did the front. The section on the pattern diagram labeled for optional lapel can be used if you want. It will fold down against the front, and the lining will show as a lapel. When you turn the vest the other way, the lining will be outside, and the main fabric will fold over as the lapel.
Sew both the lining and the main vest front and back pieces together at the side seams. Press these seam allowances open. Grade them by trimming all the allowances on the lining. Press under the shoulder seam allowances on the lining front.
Put the lining and main vest together, with right sides facing. Sew all the way around the armholes, all the way around the outside edge, and across the back of the neck. In other words, sew all around the vest except the shoulder seams. Clip the curves, and grade the seam allowances. Turn the vest right side out through one of the shoulder seams. Press.
In the nineteenth century what we call vests were called waistcoats. They usually had two pockets: one for a watch, and the other for the fob, which was essentially an ornamental counterweight to the watch that allowed the watch chain to drape between the pockets.