Two year rule for excluding long term capital gains from the sale of my primary residence

I have two homes I live in equally. I travel between the two weekly. I spend 3 nights in one and 4 nights in the other and then flip that. Sometimes I stay a week to ten days in either of them at a time so occupancy is about equal over the course of a year. I live in South Carolina and my state allows a property tax benefit for the primary home but not the secondary. I have owned both homes over twenty years and have assigned both as my primary residence over the course of those years but of course never at the same time. In fact, my wife and I have joked about getting a divorce so we could claim each one as primary. The property tax delta between primary and secondary is significant. Since we are getting older and two houses demand more upkeep, we have decided that our home that is currently classified as our secondary will be the one we should sell because it is more remote from doctors and daily conveniences. In order to take advantage of the long term capital gains tax exclusion from the sale of a primary residence, I called the county assessor where my primary residence is located to start the process of changing it to my secondary residence and was told they would be glad to give me a letter releasing that property so I could apply for the property tax reduction at the other home. I made the call in July 2020 and was told it it could be issued immediately and my tax bill would increase on that home for this year or we could wait until next year and impact the property taxes paid in 2021. Either choice will lead to a significant increase or decrease in the property taxes for each home.

Here is my question. When does the clock start on the two year period you have to own your home before excluding any long term capital gains from its sell on your tax return? Does it start on the date the letter was written, e.g. August 2020 or does it start on January 1st of the year we paid the property tax associated with it being a primary residence?