First of all, you can't deduct any property tax unless it is properly assessed to your property. For example, in New York, the legal authority for the counties to assess property taxes does not exist until January 1, with the bills due Feb 15. So technically, even if you know what the bill will be and you pay it in December, it's not legally deductible.
Assuming that both the 1/31/21 and 7/31/21 payments are legally assessed prior to 12/31/2020, the question of whether you will benefit more by paying them early is very complicated.
If you are close to the $10,000 cap on itemized state and local taxes, then paying extra won't get you a larger tax deduction. If your itemized deductions (including state and local taxes, gifts to charities and mortgage interest) are already more than the standard deduction for your status, then paying double in 2020 and nothing in 2021 only changes when you get the deduction, not the eventual amount of the deduction. However, if your itemized deductions are close but not over the standard deduction, then doubling your tax payments may get you a benefit.
For example, you pay 2020 and 2021 before 12/31/2020 and you itemize in 2020. You pay no property taxes in 2021 and take the standard deduction. In 2022, you pay property taxes for 2022 and 2023, and that helps you itemize. And so on.
Only you can do the math to really figure it out for your situation.
