You can blink. EA says nothing about doing the exercise without blinking.
Think of it like looking out a window at a tree at night. First, the tree is in focus, and can be seen clearly. Then you pull your vision back and bring the focus to your reflection in the glass. When you do that, the reflection is seen clearly, but the tree, while still seen, becomes fuzzy and indistinct from everything else.
That is the effect you are looking for, so when you pull your vision back, it might help if you imagine there is a pane of glass between you and the line and you want your focus to be on that glass a few inches in front. Once you are focused on the imaginary glass, simply hold your vision there, blinking naturally, and then drop your awareness to your breath and follow it for a few minutes. You will experience a sensation of falling and may see little streaks of light around you (what EA calls static rain). That’s the Theta/Gamma sync.
Once you are there, continue focusing on your breath to solidify the altered state. Then you can begin your summoning.
One thing to keep in mind is that TGS is NOT necessary for most magick. All you really need is an Alpha trance (if you want some easy methods for Alpha, just type “trancework” into the search bar).A deep state such as Theta is only needed for the full physical manifestation of spirits.