Tests like the one to "Say the alphabet backwards" are not designed to test intoxication but to elicit a response similar to "I can't even do that sober". This type of reply can then be used as a confession.
A police officer explained to me that some of the other tests are using testing for things other than the obvious (for instance, even if you follow the pen, your eyes jump in a way that's a tell-tale sign of intoxication)
"Vertical nystagmus". Which is all well and good, but many people have that entirely apropos of alcohol consumption.
Where are you getting that idea? As far as I know, that’s the punchline of a common joke. I’ve never heard the claim that it’s actually the purpose of sobriety tests.
What would be the best response to that? Both "I cannot do that sober" and "I cannot do that drunk" sounds incriminating enough.