Ray Raphael explores this in some detail, including tests, in his book Founding Myths, which is about myths surrounding the founding of the US, and in particular the American Revolution (I agree that American War of Independence is a more accurate name but given that Americans have been calling it the Revolution for over 200 years I don't think we'll switch our name for it). Given that musket volleys were usually first fired at a range of 50-75 yards (roughly 50-75m), and the incredible amounts of smoke generated by black powder (an issue that volley fire helped reduced but didn't eliminate) he concluded that it was a figure of speech - an exhortation not to fire until you were within a practical range but not something to be taken literally.

No expert. But in musket warfare, there was no rifling inside of their guns. Rifling are like tiny thread inside of a guns barrel that cause bullets to spin. Most guns these days have this. But back when musket warfare (for lack or a better term at the moment) was going on, rilfes were expensive and harder to provide to a whole army.

SO what this means is that the average infantryman was carrying a musket not a rifle. No rifling, so the shots would be more erratic/less accurate. Waiting to see the whites of their eyes would mean you don't miss basically. There were still instances where sides would stand some distance apart and volley at each other. But a well trained british infantryman could fire 3 shots in a minute, or that was what was expected from them. Not very fast if you think about it. 20 seconds is plenty of time for a line to advance on you, or cavalry. So holding those shots until you were more likely to hit them was a better idea, saving time and probably lives.