Use this tactic sparingly, with caution.
I used to need detailed input from a cross-level manager that was 2 levels above my supervisor in the chain of command.
For this individual and situation, the thing that worked best was to copy his manager on my requests. The first time I did this, my copies had not cooled down before he responded.
Even if you do not copy upper management, make sure that there is a clear and open paper trail that closes the loopholes that the manager uses for their lies and excuses.
Next, look at company politics.
Is there a reason that you are not getting the individuals time and cooperation?
Is there a personal conflict between you and them?
Do other projects have higher priority either to the company, or to the manager?
Is the manager opposed to your project?
Why was this person placed on your project team?
If you can determine the root cause of the lack of cooperation, it will be a lot easier to figure out the steps needed to get the problem corrected.
Have you had a closed door, but open mind, conversation with this individual about your project?
Are there other resources that could be utilized in place of this particular individual?
Chas