I put an external brake rearend in my 582, and the brake pads were shot. Today, I relined them. It's easy and cheap with some material from McMaster Carr. It's part number 6175K119 which is 3/16" thick by 3" wide. It's currently $6.96/ft. One foot will do one tractor and leave some left over. I bought 3 feet, as several of my tractors have worn brakes.
Step 1: Remove the old lining. There are several styles of external brakes used on the IH and MTD built tractors. This IH rear that I believe was originally in a 126 has holes in the backing metal part of the pads. I knocked out the pad material in the holes. I scraped as much of the old pad off as I could with a razor blade, and then I soaked them in a 50% solution of muriatic acid for 1 hour. The acid helps soften the adhesive so you can scrape the rest off with the razor blade. One pad had a really hard spot that I had to chip off with a chisel.
Step 2: Cut lining
It's easy to cut the brake lining with a utility knife. Each pad needs a piece 1.5" x 4". Four pieces are needed.
Step 3: Prepare the backing plates
After cleaning all the old lining and adhesive, I cleaned the backing plates with mineral spirits, and then applied the adhesive pictured to the lining, and then spread it into a thin layer on the back of the lining. I put plastic from a Wally World bag between the pads so they wouldn't stick together, and then I clamped them very tightly in a vise for an hour.
Step 4: Paint and install
I splattered some cheap primer and black paint on the back of the backing plates to keep them from rusting. I then installed them on the tractor.
Side note: 3/16" material is ever so slightly too thick. It was difficult reinstalling the pads, and I had to drive the tractor a bit to wear the pads a bit so that the wheels would turn easily. They'll loosen up eventually. I haven't installed one side yet as the paint wasn't dry. I may try planing 1/16" off or so to make them fit looser.