On the Form 8288 there is a withholding agents Federal identification number 13-3436547 which I assume is the number of the attorney dealing with the sale,and in the space for the identification number of foreign person subject to withholding,there is the comment 'applied for'
That answers it. Unfortunately, it will be quite a process to get this refund. What should have been done is Form W-7 should have been attached the 8288 filed by the withholding agent. Assuming this was not done, in order to get the refund of the 10% withheld (assuming there is no gain on the sale of your timeshare), here are the steps you need to take-
1) Prepare a Form 1040NR Get a US taxpayer ID number (ITIN). This is issued to taxpayers who do not qualify for a US social security number. To obtain one, you need to submit a competed Form W-7 with the required documentation. The issue is the required documentation requires you to either send the originals (which I am assuming no one wants to do) or you need to go the Embassy to have them certify the validity of the copies.
2) Assuming you are able to provide all the documentation the IRS requires, you will need to file a Form 1040NR to file for the refund of the 10% withheld (assuming $0 gain).
The IRS might ask for your 1040NR as part of them issuing the ITIN but do NOT file a 1040NR US return until they issue you an ITIN.
3) Lastly, since the 8288 that proves they withheld 10% says "Applied For" under the ID number, you will need to have the IRS recognize that withholding is yours and have the amount transferred to your Taxpayer ID account (which they cannot do until you get your ITIN issued).
So the question is, how much is the 10% withheld because if it's a nominal amount, it's just not worth the hassle.