I cannot find emails backed up by Time Machine on iMac

I do not use Time Machine on my computer as I prefer to back up manually. However for my wife's computer, we tried using Time Machine and we found out that apparently it does not back up emails. This was a deal breaker for my wife who needs to save many email messages for future reference. I investigated and found a back up app that does back up everything, including the email messages. It is Carbon Copy Cloner. It had a purchase price of $39.99. I think it can be used on multiple machines for the one time purchase. It also has some features that Time Machine does not have.