Eyes have been a learning process for me. It's hard to get eyes that don't look weird or creepy, but are still representative of a more realistic style.
Not every eye style will work for every project. Here are the different representations of eye techniques:
This is simply a French knot on top of the felt face.
This works fine for projects like this--these Firefly finger puppets don't need accurate eyes, just a suggestion of them.
Here, Leia is meant to be more cartoonish, so I simply cut out very tiny rounds of felt and glued them on the face piece.
Cartoony characters in general are a bit easier. It's easy to layer their eyes with different color felt components. They don't need to look flat or inset, because a pop-eyed effect doesn't take away from the overall look (or, in some cases, is consistent with the character).
This is a simple backstitch over the felt layer using the full strand of embroidery thread. I find it a bit bulky.
Julia also has a face under this face. Because the first eyes just did NOT work out and I had to try again.
These two are examples of the same backstitch technique, but using different strand thicknesses. The Handmaid is has 3 strands of thread from the 6-strand original, and Rosie the Riveter has 2 strands of thread and some very fine eyelash detailing.
Bob Ross and Captain Picard are examples of stitching the eye shape detailing and then doing a French knot pupil. In Bob's case, he doesn't have any additional eye fill, where in Picard's case, the whites of his eyes are stitched in. I do not prefer this technique, and if I re-did these I would use the next technique.
Cut-out eyes are tricky but the effect is worth it. Here, you cut out the eyes in the top layer of felt and then insert a small piece of felt for the pupil. This took some time to learn.
Ruth Bader Ginsberg was my first experiment in this technique. Because she has dark eyes and light skin, overall this works.
With Michelle Obama, I thought I'd try an inset French knot. So I cut out the eye holes, but I filled them in with a French knot instead of felt. This is not a bad technique, but the felt pieces were easier for me.
The first attempt didn't include whites which, in my opinion, is not a great look. I added a tiny bit of white felt filler (without gluing in), and I think it looks much better that way.
Filler also improved RuPaul's eyes. I don't glue in the white filler, I just tuck it in the eye hole. It should stay with normal use.
Princess Leia and Carrie Fisher, like RBG, didn't seem greatly improved with eye white filler. So I left them as-is--cut-out eyes with felt pieces glued in the center.
Of course, if this is all too complex, you can always take the easy way out...
And just make weeping angels.