I am trying to move the focus to the next element in the tab sequence based upon the current element which has focus. Thus far I have not turned up anything in my searches.<
Tabbable is a small JS package that gives you a list of all tabbable elements in tab order. So you could find your element within that list, then focus on the next list entry.
The package correctly handles the complicated edge cases mentioned in other answers (e.g., no ancestor can be display: none). And it doesn't depend on jQuery!
As of this writing (version 1.1.1), it has the caveats that it doesn't support IE8, and that browser bugs prevent it from handling contenteditable correctly.