Grants both Sneak and Invisible effects simultaneously. The two effects will always have identical durations.
If used when Sneak is still in effect, the jig fails entirely and have no effect. This causes Invisible to wear off and it will not be reapplied.
As with the spells, you can disable the Sneak effect manually when it is beginning to wear off and reapply the jig. Using the jig will automatically remove Invisible for you, so manually removing it is not necessary.