There's no really easy way to tell what % he might need to have withheld..
You could try the tax calculator at the following....but where it asks for 2019 values, you would put in your expected 2020 values and see if taxes due come up short or not. Repeat using it several times as you experience how it works.
https://turbotax.intuit.com/tax-tools/
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Or you could just start out at a nominal 15% or 20% Federal withholding, and see what happens when you file 2020 taxes at tax time in early 2021...then Up the % or Lower it next year depending on whether you owe, or get a refund.
IF he's started getting a pension too, if the monthly total of SS + Pension approximates his former salary, then just have the ~ same % withheld from both....same % as what Federal income taxes were being from his salary before retirement. Then adjust higher or lower after you file your 2020 taxes and know what your situation is at that time.
...or if monthly pension plus SS is ~1/2 his former salary, chop 5 or 10% off that former withholding %
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
