Cycle through spaces in Mavericks
I haven't tried it, but the app TotalSpaces2 seems to provide this feature:
https://totalspaces.binaryage.com/navigation2
Caveat:
In newer versions of macOS they require you to disable SIP when installing.
They don't cycle any more, last to first.
I've found the best solution is to assign a key command to every Space you use & go directly to the one you want.
I use Ctrl/number.
Additional irritation is that Fullscreen apps insert themselves into the 'list' of Spaces, but cannot be called directly.