The proper way to file Form 8606 is attached to Form 1040-X.
Form 8606 can be mailed by itself only when you are otherwise not required to file a tax return.
How to file:
Do not include your old 1040 nor your revised 1040 because the Form 1040-X reflects any changes there and becomes your new tax return.
Include any new/corrected document only if it shows federal tax withheld, and include in order only those Sequence Numbered tax forms and Schedules that changed or were added due to your amendment.
Attachment Sequence Number is on all the forms and Schedules that come after 1040.
If any forms specify an attachment, put all those attachments at the end in the same order as the forms they go with.
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Mail to the address shown for your location in the most recent Instructions for Form 1040-X.
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Note: when you are not changing any dollar amounts on your amended tax return, you can leave all the lines 1-23 EMPTY.
Probably this is the case here, since you tried sending it alone.
@OKevinP