The PERS mechanism sits inside a soft flesh-colored plastic plate inside of the cowl. To access the mechanism, you'll need to remove the plastic ring that holds the metallic circle at the bottom of the cowl. It is glued in place and is the type of plastic that doesn't bend much, so be careful when wedging it out of place.
Once that is removed, you can access the PERS.
Here's a rough diagram of what you'll see when looking up into the cowl at the PERS:
The red line is where the eyes go into the soft, flesh-colored plastic plate, and the space designated with the word "here" is where you can use a flat head screwdriver and push back, carefully, until the eyes pop out.
No need to remove the flesh-colored soft plastic plate, but it does make the whole process of removing the eyes and painting the lids easier. Removing the soft plastic plate is difficult though, because it is really glued down.