Placing the bracket on a folded towel or something similar will help prevent the drive rivets from flying away when they come out. The rivets can become corroded to the ID plate so I like to drive them out alternately, a little bit at a time so they don’t damage or bend the plate. A short punch will give more control than a long punch, which might bend.
This photo shows the style of rivets used but the ones in your motor will be shorter.
