Hey there! I'm so sorry we weren't here for you when you needed us. We definitely want to make sure that the available options are clear! Do you mind letting me know which page you were viewing that listed "Live chat" and displayed those hours? Our Contact Us page explains that the Message Us function is available to T-Mobile customers, and when you click the button it should direct you to MyT-Mobile to log in. Once you're in MyTMO, the Contact Us page shows something like this:
And should show options available based on the time period that you're reaching out, and your account. Is that the 24/7 you were referencing? If so, was the Message us button grayed out?
Full disclosure: we're not the team that's responsible for the verbiage on the MyTMO site, but we're happy to forward feedback if you're seeing something misleading! Now that you've found our Community, is there anything we can help you with here?