Oddly enough, I don't find myself using 'as'. Like, at all. However, I guess from my age and time period I grew up, I don't see a problem to using as.
The man squinted his eyes as he looked at Elvis.
How I always thought of this was "The man is squinting" is an action taking place WITHIN the action of "Looking at Elvis". So he would be looking at Elvis and squint, and continue to look at Elvis. He might stop squinting at some point, but continue to look at Elvis. The squinting takes place at the same time as looking at Elvis, but it did not start with looking at Elvis, and ends before, or at the same time he stops looking at Elvis.
The man squinted his eyes AND looked at Elvis
This would mean the man squinted his eyes and looked at Elvis at the exact same time for the same amount of time for both actions.
The man squinted his eyes THEN looked at Elvis
This would mean the man squinted his eyes, STOPPED, then looked at Elvis. The implication for Then is the previous action halted.
The man squinted his eyes, BUT looked at Elvis
This one is weird, because BUT implys negation of what comes before it. So he is squinting, then he is compelled to look at Elvis, which sounds like the squinting should STOP as he looks at Elvis. It is unclear in this case, and I wouldn't use it for that reason, but it doesn't mean it couldn't be used, depending on what emotion you are trying to make the reader feel.
The man squinted his eyes WHILE looking at Elvis
This is in many ways the same meaning as "As", However, I see it as meaning he squinted at the same time as looking at Elvis, BUT, it does not mean he will CONTINUE to squint, and may end squinting before he stops looking.
But that's just how I've seen them work functionally when I applied them to legal arguments.
When you are writing, sometimes you use words incorrectly to give a certain feeling or emotion.
He trod paths where plants had forgotten the sun.
Technically WRONG on every level, but I think you can get my meaning.