I faced a similar issue where time machineTime Machine was not detecting my first partition on a WD 1 TB disk but showing the 2nd partition available for backup. I erasederased the 1st partition by using Apple Disk UtilityDisk Utility and reformatted it to Apple native partition type. As soon as it finished doing that, it asked me whether I want to use this as a backup drive. I selected that and now Time Machine was able to pick this up :)