I've always considered the blinking to be going on at a rate of several times per second. So, that the character would never have time to line up a shot while on the material plane, because he'd only have a small fraction of a second.
That said, I imagine it like looking through an airplane propeller. Sometimes, the target is completely blocked, because the prop is between you and the target (or you're on the etherial plane), and certain times, the target is perfectly visible, because it's not (or you're on the material plane). But, as anyone who ever looked through a plane's propeller can tell, you can fairly easily see everything on the other side.
When you attack, you just take your chances that your attack won't be blocked by the prop (or you being on the wrong plane). But you really have no chance of deliberately timing it, because it happens so rapidly.