There is a known issue with Time Machine where a backup will show, but cannot be selected while using a secondary monitor. It still exists in 10.9.2, but fortunately we have a few suggestions for how to fix it listed below.
My first suggestion is unplugging the second monitor, launching Time Machine and restoring the file, then plugging the monitor back in. This is not necessarily the nicest solution, but it does save having to log out and back in after making changes.
Other ways to resolve this involve changing monitor settings. First, try switching monitors to mirroring mode which seems to resolve the issue for some folks. This option is in the Displays preference pane shown below:
Screenshot courtesy of Adam Christianson and his HP Monitor. We don’t judge.
Another way to fix this is to hop over to Mission Control and uncheck the ‘Displays have separate Spaces’ option, which sets displays back to the way they used to behave. This change requires a log out/in to take effect, but again is a method that has been reported to work.
Screenshot of Mission Control.
We speculated about this in the TMO Towers, and came up with the following theory: this problem occurs because in the old days Time Machine always ran in full-screen mode on the main screen, before there was even an official ‘Full Screen Mode.’
Now Mavericks lets you do this “run an app in its own space” thing.. Assigning those spaces to separate monitors is awesome because it creates the option of separate full-screen apps on each monitor. Well, it’s awesome until you need to restore, because Time Machine doesn’t like it at ALL. Any time it’s set up is the time when Time Machine fails.
Using the steps below, however, should allow you to correct it.
Image made with help from Shutterstock.