Replace only as much as you need to- if you can get away with a small section, then go that route. If you start digging into it and find it's worse than thought, replace a larger piece of it. The difference between a small piece and a large piece will also be dictated by which is physically easier to do. It doesn't make sense to spend tons of time repairing a section when the entire piece can be replaced quick and easy, right? In your pic it almost looks like you've got pinholes on the bottom side too. I'd recommend cleaning and grinding the paint off 1st, tap it with a pointed hammer and see if you go through anywhere, then replace as needed.
Working on old cars teaches us patience... and every curse word imaginable!