Format Matters
My problem is that my external drive is showing up in the "exclude" part of the Options, but Time Capsule will not allow me to remove it.
Cory, or anyone else with this same issue, it depends on the format of the external hard drive which is plugged into the Mac to be backed up to the Time Capsule.
Mac OS Extended (Journaled)-formatted drives should show up automatically in Time Machine Preferences > Options > Exclude list, in black letters, with the option to remove it from the exclude list. Removing it from this list allows that external hard drive to be backed up to the Time Capsule's internal hard drive, as long as the external is turned on and plugged into the Mac that's backing up to TC.
If external hard drive is formatted for MS DOS, also referred to as FAT32, then it will appear in the exclude list as grey, and will not be removable. Your option at this point is to reformat the drive to Mac OS Extended (Journaled), which erases everything on that drive, so if your end goal is to back up existing data which currently resides on that drive, you need to have a solution for getting the existing data off before you reformat. Another external hard drive or a computer with sufficient space will do, and drag and drop should work. On a Mac, you can reformat an external hard drive in Disk Utility's Erase tab.
I've not yet tested an external hard drive formatted for NTFS, because I do not own a computer running Windows. Please take this last statement with a grain of salt, but I would imagine it would also show up greyed out and unable to remove from the exclude list.
I hope this clears up some confusion for anyone who wanders upon this, as it does seem to be a question many people ask in the wonderful world of wireless.