There is no such thing as a Thunderbird email account. Thunderbird is email client software that runs on your computer. It is not an email provider or service. You can install Thunderbird software on your 2nd computer and enter the details for your real email account and access those emails just like you do now. Just be aware of the differences between an IMAP and a POP email account. IMAP is server based and you just remotely view the messages that remain on the server. This is geared for people that need to check their email from multiple devices. POP emails are downloaded to your local computer when you connect to the server. You have the option to leave those messages on the server or delete them from the server after downloading them. If you download them to one computer and delete them from the server the 2nd computer will have nothing to download when you check your messages.