The Picard Manuever could only work if the attacking ship thought that the other image was a hologram or some sort of illusion.
The problem with it is the FTL sensors. They are not dependant on the speed of light by definition so they would only read one ship. Plus they would detect the burst of energy from the warp engines so there is no reason for any FTL ship to not know which one was which.
So the only way it would work is if they had been previously tricked into firing at a hologram and they thought this was another example. Of course their weapons would be tied to their FTL sensors so they would probably not fire at the original location even if the crew wanted to because there would be no target there. They would have to go to manual to make it work and by that point the image change will catch up with the ship.
When they showed it on the show the ship was only a lightsecond at most away so it would have only appeared for a second.
Of course having known about it would have automatically negated the whole tactic so the Ferengi were being stupid to fall for it but the Enterprise crew was MORONS for even considering it a problem.
It was just a case of writers with no good idea for a tactic doing something silly.