Well, let's see. Did the Ferengi have FTL sensors? Yes, it must have in order for them to lie in wait at a moon, spot the Stargazer traveling by at Warp 2 and then catch up and attack it.
Not necessarily. It's a bit more likely that Stargazer dropped out of warp for a moment -- for whatever reason Picard didn't bother to mention -- and the Ferengi ship dropped out of warp at point blank range and opened fire.
Picard was pretty clear in saying that they were "traveling at warp 2 through the system".
And what was required of the Picard Maneuver?
1. High Warp
2. The Enemy choosing the wrong target to fire at.
3. Possibly some kind of timing for a sensor bearing "return arc".
The wrong choice doesn't seem all that relevant, it's just something Riker happens to find really amusing. Data even says, later, that there is no known counter to the Picard Maneuver, which implicitly rules out "just fire at the closer image."
But what does that mean about no known counter? Does that mean no known defense to it or no known counter-attack to it? Riker's choice in addition to the tractor beam is focusing the shield protection as well. It could be no known counter to the Picard Maneuver includes the inability to allocate shield reinforcements.
RIKER: Right. Concentrate shields at that point. Make it so. I hope you're right, Data.
The logical conclusion is that the maneuver works the way it does because theoretically you don't have time to fire on EITHER image before your attacker cripples you, in which case it was the Ferengi's last spiteful shot -- as their ship was exploding around them -- that was aimed at the wrong target.
That cannot be the case since the dialogue states the Ferengi chose the wrong target and when same maneuver is used on the E-D they clearly had time to see the action. However since weapons lock and fire still require human interaction it may have been too slow for Worf to make a decision and push the necessary buttons (as his reaction) to use the tractor beams. Data, or the fore-knowledge of the maneuver with computer preset, could beat the timing as seen in the episode.
How does "seem to disappear" fit into this?
It's what Data says later in the episode when Stargazer tries it on the Enterprise. The clear implication is that under normal circumstances you cannot track a starship moving towards you at high warp speed.
Right, "high" warp speed. Not just any old "Warp 1" hop.
The main viewer does show that the E-D had no problem tracking the hop though.
AFTER Data reprogrammed the sensors to scan for a gas compression and focus their attention on that. Under normal circumstances, there'd probably just be a flash of light as the second Stargazer image suddenly appeared and opened fire.
By scanning for the gas compression, the sensors are still reporting back in the FTL movement as it was tracking the movement vector in real-time. So, still FTL sensors are in play.
And again, the issue is that the sensors won't detect Stargazer's new position until it drops back to sublight speed. The whole while it's at warp, it appears to still be sitting in its original position, not moving at all. Scanning for a sudden compression of gases gives those sensors just enough warning -- milliseconds, really -- of where stargazer is about to be.
I would argue that the sensors are at a minimum tracking the new position because it is animating the warp lines (or direction) in real-time prior to the new image solidifying. The issue is that the sensors or computer does not erase the old image which would suggest that it had not refreshed it's position data and treated them both as legitimate targets for a brief moment.
If we were to put together a picture of the battle in Picard's own words:
PICARD: We were traveling at warp two through the Maxia Zeta star system when this unidentified starship suddenly appeared and fired on us, point-blank range.
RIKER: Where did it come from?
PICARD: It must have been lying in some deep moon crater. First attack damaged the shields. In the confusion, they hit us a second time.
TASHA: No clue who they were?
PICARD: No names, no reason. Can you identify them, Vigo? If they come in a second time with our shields damaged
TROI: Sir? Who's Vigo?
PICARD: He's my weapons officer on the Stargazer. I'm getting quite caught up in this.
RIKER: Your shields were failing, sir.
PICARD: I improvised. With the enemy vessel coming in for the kill, I ordered a sensor bearing, and when it went into the return arc
DATA: You performed what Starfleet textbooks now refer to as the Picard Maneuver
PICARD: Well, I did what any good helmsman would have done. I dropped into high warp, stopped right off the enemy vessel's bow and fired with everything I had.
RIKER: And blowing into maximum warp speed, you appeared for an instant to be in two places at once.
PICARD: And our attacker fired on the wrong one.
And how Picard remembers it in the chronological order prior to executing the maneuver:
PICARD: Damn, I said put fusion generators under surge control. You're moving too slowly. Arm the torpedoes, man!
Vigo! Get a fire control party up here!
VOICES [OC]: Shields weakening, Captain! Fusion generator online.
PICARD: Weapons report!
VOICE [OC]: Phasers coming to full charge, sir. Torpedoes armed!
PICARD: Who are they? Identify them!
VOICE [OC]: They're coming for a third pass at us, sir!
VOICE [OC]: We can't take another hit, Captain!
PICARD: Damage report!
VOICE [OC] Fusion generator under surge control, sir! Power systems failing!
PICARD: Sensor beam bearing on hostile ship!
VOICE [OC] Seven mark nineteen, sir!
VOICE [OC]: Phasers, sir? Sir?
PICARD: Ready phasers, and lock! Stand by on warp nine. Heading seven, seven mark twenty. Engage.
PICARD: Steady. Now, reverse and stop! Phasers fire, torpedoes away! Fire. Fire.
In the final moments we do not know if the Stargazer was still at warp or at sublight but they jumped to Warp 9 for the maneuver. But we can see from the dialogue that Picard and crew were following whatever maneuvers the Ferengi were doing during the attacks.
In re-examining the episode, it reads more like the maneuver uses a sudden high warp move to confuse enemy sensors, both FTL and LS and the computers that monitor them leading to forced errors on the enemy crew. It does not appear to be a FTL ship taking advantage of LS sensors, IMHO.