Fasting test for T1 and T2 have slightly diferent reasons behind them..
Even the T1 fasting test, will be slightly different for different regimes...
For T1's that inject a per-mixed or on a 2 injection a day, there is a need to match carb intake to match insulin injected, so a fasting test is carried out in the morning upon waking, otherwise there is a real danger of putting someone into a hypo situation.
For T1's that use basal/bolus regime with injections or with a insulin pump...
The fasting fasting testing (apart from your normal before breakfast BG) is carried out over a period of 12 hours, at different times of the day, this is carried out to see it the dose or in the case of a insulin pump the basal program is correct and is keep the basal line correct... And you fast for 12 hours depending on what part of the day you're are checking, and you Take a BG every hours, not only to check if your BG is steady but to ensure that you are dropping into hypo, or your BG's are getting too high, these two later ones you would have to stop the fasting and take action to correct.
For T 2's
Fasting tests are normally carried in the morning, as this should show what your normal (lowest level) would be either diet or with medication.. Due to how mainly oral medication works within the body and is mostly taken with a meal, fasting durning other parts of the day really wouldn't effect or change (on a daily bases) the medication side of things...