I noticed that Ikea's Skadis pegboards are perfectly sized to fit within their Billy bookshelf, so I made a part to help hang them. I used the 30" x 22" pegboard for the wider bookshelf and the free-standing 22" x 14 ½" pegboard for the narrower shelf. The 22" x 22" board would also work.

This solution repurposes the existing holes and metal pegs used for mounting shelves, so no drilling or extra hardware is required. To install, press the metal pegs from the bookshelf into the two holes on the printed part, then press that into the holes at a height that aligns with the pegboard slots.

This solution allows two possible depths for hanging the pegboard, using either the front or back row of holes. The mounting hole is sized so that Ikea's mounting screws are self-tapping - I haven't had an issue with this so far, but you could also use an M4 nut on the back for extra strength. You may have to dial in the fit of the pegs with a drill or employ some hammering depending on your printer settings.