Bad ticket, only sticks if it's 7mph or over the speed limit.Contest it, Go to court and have them summon the speed census for the street you were on and the last record of radar and speedometer calibration for the car that pulled you over. They won't show, and with the lack of evidence, and the not 7mph over, you'll be god to go.
As for the OP issue, the sobriety tests are bullshit. All it is for is to check that you can do something while listening, since being intoxicated limits your motor functions and concentration to just driving (usually). The cop will use their judgement to see if you can basically multitask. The sobriety tests are all designed to check your multitasking abilities, that's why they talk to you while you do the tasks, to see if you're paying attention and understand what they're saying. Usually, the eye-chart will key off the test. They hold a card up to your eye and check with a flashlight your pupil size, then if they have determined you're drunk, they will give you the sobriety test. They already are going to put you off the street before they even do it, then you have a chance to redeem yourself. The thinking behind it is that just because you're BAC is .05, doesn't mean you can handle that. .08 is usually a good arrest, but that's the "limit" just as there's a speed limit, not really intended to drive that fast, just not go over it, and yet you can still get pulled over for going under the speed limit if the conditions aren't safe. Same idea. All about judgement calls.