After taking care of my elderly father, he passed away Oct 2021 and I am now his fiduciary. No final income tax return is required, but I do need to file a final Form 709 on his behalf with my signature. 

To which address should Form 56 be mailed?

Instructions for Form 56 state:
https://www.irs.gov/instructions/i56
"File Form 56 with the Internal Revenue Service Center where the person for whom you are acting is required to file tax returns."

There are two mailing addresses given for California for income taxes:
https://www.irs.gov/filing/where-to-file-addresses-for-taxpayers-and-tax-professionals-filing-form-1...
"Form 1040 and Form 1040-SR addresses for taxpayers living within the 50 states [...]

And you are not enclosing a payment use this address:
#1 Department of the Treasury / Internal Revenue Service / Ogden, UT [...]

And you are enclosing a payment use this address:
#2 Internal Revenue Service / P O Box 802501 / Cincinnati, OH [...]"

Is it correct that Form 56 should be mailed to the Ogden address, or might the IRS require I send it along with the gift tax return instead (Department of the Treasury / Internal Revenue Service Center / Kansas City, MO 64999), as there will be no final income tax return?

If it should be sent to the Ogden (or Cincinnati) address, how long might it take to process Form 56, and would it be a good idea to send in a copy of it with Form 709 to Kansas just in case they might otherwise process Form 709 before Form 56? My concern is there could be a chance they reject my signature on the gift tax return if I am not in the system as a fiduciary yet.

Thank you.