Hi arrow1, and a warm welcome to OutdoorKing. It's great to have you aboard. I have tried to do a bit of research for you, but unfortunately, there are at least 7 different models (most probably more) of the Mac Cat; without its exact model number and serial number its going to be hard to pin down a part number for the brake band.
From what I have learned the saw was manufactured between 1985 and 1989.
My advice is to maybe take it to a reputable chain saw repair shop and hopefully one of the old hands may be able to identify the model and advise on the availability of the spare part for you.
Sorry I cannot be of more help,
Once again, Arrow,