Besides the System Clipboard, how can I view clipboard history for the other clipboards? Right now when I enable the clipboard switcher, I can only see clipboard history for the System Clipboard.
The Clipboard History Switcher should show you the last 200 items you have copied.
If you are only seeing the current one, then I would guess that you have changed a setting. Either you have excluded the current application and it is not copying things (but then you'd still have clipboard history from other apps) or you have actively set the clipboard history length to 0 or 1 with the defaults write command described in Preferences user manual section.
If you're looking for the named clipboards, try Shift-Control-C to Activate Named Clipboard Switcher in the Switcher Group that also contains Activate Clipboard History Switcher (which it looks like you're familiar with).