had to give up on the 1st eye level - it seems impossible to get up the right hand side of the screen without getting hit by either the spikes or the eye ? was enjoying it up till then !
You have exactly 7.5 seconds before the eye starts to open. The eye will only kill you when it's fully opened, and once it starts to close you are safe. It's like you have some iframes while it opens or closes. It's true, the right side jumping area takes around 6-7 seconds to do, so it is better to wait the perfect time to start it and once finished stop again to wait for the eye. There is no randomness of the eye, so it won't randomly open before 7.5 seconds or so, however every level uses different time.
Also, thank you very much for trying it out. It means a lot, and your feedback is very valuable, the game is intended to be difficult in some cases and requires some trial and errors to do, but if you really feel that a level is unfairly hard, I will consider to change that.
Here is a little video, hopefully this helps you a bit.