In TSPE McCawley argues that time adverbs can modify V' or can undergo a rule he calls "Raising" and come to modify S. So there is not necessarily a determinate answer to your question. I found an argument that the "while" clause need not modify the whole sentence, because its subject is commanded by the subject of the main clause. That is, the following sentence structure is possible:
I [am unable to join you while I am on vacation]
The argument is as follows. There is an interpretation of this example,
I am unable to join you while I am on vacation, and so is my sister.
in which the meaning is:
... and my sister is unable to join you while she is on vacation.
That is, I and my sister are not necessarily on the same vacation at the same time, and what I and my sister have in common is not being able to join you while we two are on our respective vacations. (If you prefer "and neither is my sister" in the above example, it doesn't make any difference to the argument.)
Thus the "so" of "so is my sister" does not have precisely the identical interpretation as its grammatical antecedent "be unable to join you while I am on my vacation". Where the antecedent has I, the sense of "so" has she.
This phenomenon was dubbed "sloppy identity" by John Ross in his dissertation, and requires that the items which differ between antecedent and interpretation of the corresponding pro-form must be commanded respectively by coreferential NPs.
So, we know that the second "I" in the example is commanded by the first "I". If the "while" clause were a sentence modifier, the structure would be:
[ [I am unable to join you] [while I am on vacation] ]
and the first "I" would not command the second "I". This is evidence that on one interpretation, the "while" clause is not a sentence modifier.