Thank you for clarifying your question @jfmp.   To allow for you to get the most accurate tax withholding, I would suggest that you add in Step 2 (ii) of the W-4P, the $20,000 amount that you receive as a distribution annually from the 403 (b) plan.    

I would suggest using the W-4 calculator here: https://turbotax.intuit.com/tax-tools/calculators/w4/ estimate what your taxes will be when you file 2023 taxes in 2024.   You just would be entering the pension income from both pensions as well as the withholding from the 403 (b) to date.  This would give you a rough idea of how much taxes should be withheld from the $60K pension distribution.  

All the best,

Marc T.