Ikea Skådis wall spacers in the original 20 mm length, as well as longer lengths.

The image shows 30 mm version on the left and the original wall spacer on the right.

For extra support, I fastened a 10 mm thick lath to the wall with screws into the wall studs, and then screwed the Ikea Skådis pegboards through the lath and into the plaster wall. This meant that I needed longer wall spacers at the bottom of each pegboard, compared with the ones that came bundled with the boards. I made a 3D printable version in Fusion 360 with a length parameter, and printed wall spacers with a 30 mm length. In case anyone else finds this useful, I've also exported STLs for 20, 25, 30, 35, 40, 45 and 50 mm lengths here.

The screw hole dimension is M4.5x0.75, which I found to be a good fit for the bolts coming with Skådis.