Here's a picture of the drill bit I modified to drill parking brake linings. I used a 13/32" drill bit, chucked it in my lathe, then used a grinding stone in my Dremel to grind the last 1/4" of the bit down to .195". I then used a collar stop to set the depth of the rivet head pocket. The collar to the 13/32" bit edge depth is .700"
I spread the band slightly before clamping the ends of the lining to each end of the steel band. This will ensure the lining is tight to the band as it's drilled and riveted.
I'll add in the information from the link above, so it will be altogether with the tool picture.
I cut the lining to the correct length then clamp it to the band. Get a drill bit the same size as the rivet shaft and drill a couple holes (from the band side) in the center of the lining. Get another drill bit the size of the rivet head, or a hair larger. I used my Dremel to grind the end of this drill bit to the rivet shaft size. This will act as a pilot. This smaller diameter will now fit in the just drilled holes, and the larger diameter of the drill bit will make the counterbore for the rivet head. I grind the larger bit angle to match the angle on the underside of the rivet head. I use a drill stop to limit how far the counterbore goes, which is about 2/3 the thickness of the lining. Now, go ahead and rivet those couple holes in the center, then expand the band some and reclamp the ends. By expanding the band and reclamping, this will insure the lining is tight to the band when it's in the correct mounted position. I alternate from side to side working my way out from the center. To speed things up I use a drill for each of the 2 drill bits, otherwise you're doing a lot of bit changing (2 changes for each rivet).
When you're done riveting, bevel the ends of the lining a little.