Hello evp58,
Thanks for reaching out in Apple Support Communities. We're happy to help.
We want to make sure we understand, when you say the backup doesn’t restore your information, are you referring to email accounts? Or, the email accounts are restored, but the actual contents, the emails received and sent are not restored?
Here are a few articles that should be helpful.
- Recover files using Time Machine and Spotlight on Mac
- Recover all your files from a Time Machine backup
Reach back out if we can help further and let us know more details.
Have a great day!