I have quite a few different Gaillardia this year and I think the seed saving is the same for all varieties...

I've been testing mine for weeks now and I think I can answer your question -

Wait for the fuzzy balls to look white. At this point, the ball will have released most of the old petals and the seed will have matured. I think the seed is immature prior to this because in my garden, the seeds were pure white. After the petals were gone, there was visible color in the seed. If you wait long enough, you'll see the seed actually separating from the ball.

I googled Gaillardia seed photos and this found this link:

http://eng.fanweb.ca/images/Gaillardia%20copy.jpg/image_mini

Some Gaillardia is a hybrid and saved seed may not be true or even viable. I have a Tizzy plant that is new to me so I haven't tried to grow the seed.

I have Goblin and Fanfare from last year and it seeded itself. The Goblin is everywhere now.

Saving Gaillardia seeds is the easy part. Getting them to germinate is trickier. I DO wait until I see a little darkness at the core of the fluffy ball. then I cut off the head and let it dry. After it's dry, I squeeze the seed head untill the seeds come off.

The thing to remember when planting, is that the seeds should nor be buried. They need to lodge on top of the soil, with the white fluffy stuff sticking up.