If you are able to chase a peagawk into a corner, you can pick it then you can leave. Once it goes into bush form, it regrows it's feathers so you can get a bunch of feathers off of the same peagawk.
Steps to Reproduce
Chased a peagawk into a corner and picked the peagawk then walked away. Repeat
Chased a peagawk into a corner and picked the peagawk then walked away. Repeat