I was thinking about casting mage hand while hidden to do things like, for example, pulling a lever behind a guard's back. But if I'm not an Arcane Trickster, the hand is visible and the question is, does it have any kind of “spectral” connection to me as its caster?
The spell doesn’t say anything about a visible connection to the caster:
A spectral, floating hand appears at a point you choose within range. The hand lasts for the duration or until you dismiss it as an action. The hand vanishes if it is ever more than 30 feet away from you or if you cast this spell again.
You can use your action to control the hand. You can use the hand to manipulate an object, open an unlocked door or container, stow or retrieve an item from an open container, or pour the contents out of a vial. You can move the hand up to 30 feet each time you use it.
The hand can't attack, activate magic items, or carry more than 10 pounds.
But in Xanathar's Guide to Everything, on page 127, this picture appears. The hand seems to have a connection back to the caster, showing the source and where they are:
Does that mean that everyone can see where you are hiding if you use your mage hand? Can they always trace the mage hand back to its source?
Or is the artwork in the book not “approved” rules-wise?