Ignorant of

Perhaps it's not the most common usage, but there's nothing wrong with it. Ignorance can be very general, or it can be very particular.

RobertB said

Similarly, used as same as 'not knowing,' are these also similarly odd?

Ignorant of which road to take

Ignorant of what time it is

Compare these that should be clearly good:

Ignorant of Geography

An ignorant population

I believe "ignorant of" will always mean "not knowing."   "Not knowing" may be substituted for "ignorant of" in every example you gave.

I would be very surprised by 'I am ignorant of what time it is' ---would be sure giveaway of foreigner.

Robert said
I would be very surprised by 'I am ignorant of what time it is' ---would be sure giveaway of foreigner.

 

It would not be the first time someone has thought my Texas way of speaking sounded like a foreigner but I don't think that phrase is unique to my area.   I have used it on occasion.   It is more common to say, "I don't know what time it is," but sometimes, just to change things up, I will use "ignorant of" to describe various things.   I may use it more often than I think because I frequently find myself ignorant.