Do you think that you could switch the plastic pull tabs to go down towards the chin? You might be able to hook up a chin strap on the ends that would pull the eyelids around. Then you wouldn't need any kind of actuator. I'm not sure how you could make it wink, but it should be able to blink at least.
Otherwise I'm not sure how you can make them move without some sort of actuator. You said that you were using solenoids, which would require some sort of wiring and (I would think) a more complex control algorithm than a servo. Micro servos should fit inside the head without taking up too much room.
To fix the problem of the plastic strip bending you could add more braces so that it can't buckle. Also, as long as you have a bit of room between the front of the mask and the wearers face, you could shorten the plastic strip and store everything in the forehead.
Another option would be to put tiny motors to the side of each eye. They would have a gear on the shaft that would mesh with the sides of the eyelashes.
Thats awesome, you knew whats happening from just that brief description and the video.
I'll respond to your reply part by part.
1) having the tabs be pulled down by the chin is the smartest idea I've heard so far.
I've been trying to use electronics the whole time, i only spent very little time to think about analogue means.
I shall look into it. At least that was a real breakthrough from my stuck situation.
2) The thing about servos and why I tried to avoid it is because of the programming and extra mobo required inside the mascot.
I don't know the programming yet, and I think you mentioned in the last point the servo will need a gear/cog meshing with the side of the eyelid thing in order to work.
Thats a lot of high precision assembly there, might not be as easy as it would seem I thought, and I wanted to find a simple and repeatable process thats why.
3) Preventing the plastic strips from bending, I thought of adding more buckles too.
That would be the natural next step I guess.
The issue I had is that, since the direction of the sliding strips is along a curved surface, there is already a lot of resistance caused by friction.
The small solenoids I have I'm afraid doesn't output that much force.
The current plastic sleeve that its sliding in now is already giving it a hard time.
I must try to find a way to make the sleeve looser I'm thinking.
I'll think of something for an analogue design.
That is a REALLY good idea, you have no idea how good it sounds to me now.
I've tried building and thought experimenting with a lot of electronics means.
But because how rough this handmade mascot head is, a lot of functions that would happen in theory doesn't quite happen in real life.