My office is located in an area that receives a lot of wildlife traffic - herds of deer, porcupines, skunks, hedgehogs, various smaller critters, and lots of rabbits. Sometimes, when I leave my office at night, I can see rows of little glowing eyes along the road. 
During the day, it’s difficult to spot the rabbits UNTIL they start to run away. The cottontail rabbit survival strategy is to remain absolutely still until discovered and then zigzag away. However, their bright white tails are an instant giveaway and it’s easy to track them after that. What kind of survival mechanism is this? How does it fool a fox - a predator whose visual acuity is similar to our own?
It doesn’t – but rabbits are extremely agile and quick. Plus, they multiply like rabbits. We have some newly born bunnies around and they are about as cute as they come.
Plus, although foxes are routinely described as having “keen eyesight”, few mammals can see even nearly as well as homo sapiens sapiens. Until foxes can see 20/20 in full colour, there won’t be anything to select for darker cottontails. A bright white tail offers a rabbit a better shot at mating than being eaten, though both happen often enough.
I noticed a similar thing with Gazelles; when pursued by predators, the herd splits up, but they have bright white patches on their rumps and they do this manic bouncing thing, leaping very high into the air; on the face of it, this seems like a tremendous waste of energy- they certainly could escape fasterif they just ran but apparently it’s saying to the predator ‘I am extremely fit and healthy, choose someone weaker’
My understanding of the reason for the bright white tail when running (whitetail deer have it too) is that it serves as a warning flag to other members of the species. “Heads up, everybody, I’m running away very very fast! And you might think about doing so yourself…”
The point of the cottontail flashing its namesake when evading predators is to confuse them. Predators that hunt by sight can easily track something moving in a straight line and follow it accordingly. They will focus on the prey; calculate its path, and pounce at the right spot. Rabbits tend to run in a zigzag pattern, flashing their tail periodically. The predator will focus on the tail, which stands out against the dull background. But the predator will be confused and be unable to discern the movement pattern of the rabbit as the rabbit flips the tail up and down. White-tail deer employ a similar defense.
I’ve heard a couple of theories about the gazelles. One is the “see how fit I am” idea, another is that with a whole herd doing this at once it’s very confusing to a preditor. Both of these apply to a herd animal, I don’t think either makes much sense for the solitary cottontail.
I think part of that strategy must be that the number of times each cottontail mates will, on average, be greater than the number of times each cottontail is eaten.
I don’t think flashing the tail has much negative fitness. If you’re a hungry wolf or whatever, and you don’t see the wabbi… I mean, rabbit, until it’s running away and flashing it’s tail, you’re probably too late to catch it.
In other words, what does the rabbit or deer care if you see it when it’s heading away from you at full speed? Remember, the rabbits and deer are faster than whatever is trying to eat them.
So regardless of what the advantage is, any disadvantage is pretty slight.