How does the 2 out of 5 year rule work when 1 co-owner has been living in the house?

[Kyle Nacci]

My ex-wife and I co-own a duplex in Providence. We're both on the deed but just I am on the mortgage. I haven't lived in the house since we separated at the beginning of 2022, and she has continued living in it, managing the property, collecting rent and paying the mortgage. I've spent most of my time in Austin since March of 2022, but didn't get a Texas license & registration until March of 2023 and haven't paid my taxes for this year yet (filed an extension).

The terms of our divorce state that my ex-wife will continue to act as owner of the house between now and September 1, 2025, and at that time we will divide our ownership of the duplex. At that time or any time afterwards, either of us can request to be bought out and - if the other party is unable to buy them out - force a sale.

By September 1, 2025, it will have been more than 3 years since I've moved out, but not more than 3 years since I got a Texas license & registration (not sure if that's what they'd look at for tax purposes), so my question is: if we sold at that time, will my ex-wife &/or I be exempt from paying capital gains tax? Or would one or both of us have to pay it?

Also, is the capital gains tax deducted from both of our profits at the time of the sale, or is it for me to pay when I file taxes? If the latter, am I correct to assume that I'd only owe capital gains tax on my half of the profit?