Time Machine Backup Logs

Psilocybe wrote:
Is there a .plist with backup logs defining to what location time machine backed up, and when?

This may not be exactly what you want, but if you launch the Console utility, select "All Messages" in the "Log List", and search for "backupd" (without the quotes), you'll see a series of messages from Time Machine. Some of them may contain the information you want.

Psilocybe wrote:
I forgot to add I'm not booting up from this recovered HD, I'm simply looking at it mounted.

Use either a command in a Terminal session or the Finder menu option Go -> Go to Folder to visit /Volumes/<thatothervolume>/private/var/log . Then look in the file system.log for such messages.

If you're talking about the failed recovery of the TM disk in your other post, no. Time Machine backups do send messages to the system.log on the Mac being backed-up, as the others have noted.

There is a hidden text file named .Backup.log in each dated backup folder inside Backups.backupdb, though. And only the system has read rights to it, so even if the recovery process found it, it may not have recovered it.