After you file

That is correct.  A 1040X is required when changing from a previously filed deductible contribution to a non-deductible contribution and visa-versa, both of which will change the taxable amount and require an amended return.   Both the 8606 instructions and 1040X instructions specify when a 1004X is required.      When only reporting a 8606 that was missed and there will be no change in the taxable amount (a tax return not required), the 8606 can be filed by itself.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**