This question is pretty straight forward. Why do Jedi or Sith say something when they uses Force Persuade/Mind Trick? One example from Episode IV: "These are not the droids you're looking for." I know that Force users lift their arms and stuff to help them concentrate, but I don't think that speaking would work the same way, because they are not exerting very hard to persuade someone. Yoda in Episode II had to make a great effort to catch the pillar before it fell on Obi-wan and Anakin. Ben Kenobi isn't seen to need to make such a great effort in Episode IV.
The Jedi Mind Trick (or Force Persuade) relies on a light touch upon the mind, and therefore is more akin to a powerful hypnotic technique. Much like hypnotic suggestion, the Mind Trick clouds judgement, making the target susceptible to suggestion from an outside source (thus the suggestion has to be made subsequent to the initial clouding of the mind).
The suggestion is almost always spoken (although theoretically I suspect it might work on some visual cues, such as pointing in a specific direction).
The Mind Trick is not really a Light Side use of the Force. Instead, its use tends to be in the grey area in between. During the Thrawn Trilogy, Luke expresses some concerns over continued use of the Mind Trick, as, at its basis, it is subverting the will of the victim, which skirts dangerously close to the Dark Side.
Indeed, it isn't too far of a stretch from the Mind Trick to Mind Control, which is a Dark Side power, and extends the power to full domination of the mind. The insane clone Jedi Master, Joruus C'baoth (who had embraced the Dark Side) used full Mind Control to dominate entire fleets of Imperial soldiers, to improve their coordination in battle, and also demonstrate his power to Admiral Thrawn. When doing so, C'baoth did not have to speak, or even be within sight of the victims of his dominance. Instead, he simply manipulated the Force to directly control their thoughts.
The distinction between a light touch to cloud thoughts, and full dominance, is why Jedis must speak or otherwise provide external commands, and Sith and Dark Jedi may skip the intermediary step of external commands altogether.
A Jedi may have the ability to skip external commands, but doing so would be a gross violation of another sentient being's will (as opposed to the a minor violation reserved for only situations where the greater good demands it), and therefore squarely on the path to the Dark Side.