Do I need to amend my 2019 tax return to indicate that the 2019's $6,000 Traditional IRA contribution happened sometime between 1/1/2020 to 4/15/2020?
A nondeductible traditional IRA contribution is required to be reported on Form 8606 Part I. In this case, this will result in the contribution shown on line 1 of your 2019 and flowing to line 14. Line 14 of your 2019 Form 8606 carries forward to line 2 of your 2020 Form 8606 to be used in calculating the $0 taxable amount of your $12,000 Roth conversion in 2020.
You'll need to file the 2019 Form 8606. You can generally do that stand-alone since Form 8606 has a signature block.
In 2020 TurboTax you'll need to indicate that $6,000 is your basis in traditional IRA contributions made before 2020.
