Hi everyone! I tried the partition thing and it worked! Here are the details of what I did, just in case you have the same issue:
I found answer ID 3865 and basically followed those steps. I selected the “Instructions for Mountain Lion.” Some of the screens looked a little bit different, but it is fairly easy to find the selection referred to in the original answer.
In Step 3: Instead of selecting 1 partition , I selected 2 partitions. I named one of them “Time Machine Backups,” and the other partition “External Drive,” but you can name them whatever you want.
In Step 4: I selected “GUID Partition Table” because I saw that somewhere on my original Time Machine. This step seemed a bit weird because you’re not selecting “Apple Partition Map,” although it’s an Apple Computer. The Apple Partition Map might work, but I did not try it, so I can’t attest to whether or not it works.
After following the rest of the steps and the formatting was complete, I started a Time Machine Backup. When it asked for the drive on which I would like to create the Time Machine Backup, I selected the partition I had designated for “Time Machine Backups.” So far, it seems to be working fine, although the backup wont complete until later tonight…
I have also tested copying and moving files to the other partition, and that works fine as well. I’ll wait until the entire backup has completed before I actually move my picture, video, and perhaps some non-essential files to my “External Drive” Partition.
Hope this helps someone!!!
Dan