Restore iPad from older backup
I had my iPad wiped while on vacation because the wrong access code was entered too many times. (lesson #1: unpair bluetooth keyboard from iPad before throwing them in a bag). So my only option was to wipe everything and restore as new. Now being back home, I wanted to restore from the backup I had made on iTunes just before I left. Unfortunately, I did not check the "Prevent iPods etc from syncing automatically" in iTunes prior to plugging my iPad (lesson #2), so iTunes did a backup before I could realize what was happening. So now, I have only one backup available: the one just made, which is useless.
I do regular backups of my mac with Time Machine, so I'm hoping there's a way to get the older backup by accessing the files on TM. Only I have no clue where to look or what to look for. Help please?
Thanks!
iPad mini Wi-Fi, iOS 7.1.2