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The tax treaty Article dealing with this income will be Article 18 paragraph 1. Here is a link to the tax treaty.
This entitles you to a 15% tax withholding rate. I would complete part II as follows:
Line 9 - check box A and indicate Australia
Line 10 - fill in the following
For the explanation: A 403(b) plan distribution is a pension since it includes compensation for services performed in prior years. Those services were performed in the US.
Question 8 in part 1 - You may leave this blank for the withholding agent to complete.
Part II b - If you are providing a Social Security number or ITIN check the box.
I am sorry to report that the answer provided by you is not correct and was not accepted for a lower withholding tax of 15%.
Sorry to hear that Vanguard did not accept the form. It is correct as we discussed. However, you will be able to claim the lower tax rate on your US tax return and claim a refund for any difference.