Unfortunately, sensor or injector faults will definately not cause any sort of light illumination at all, only in total failure have i found the lights illuminate.
It could be the pump but as it is revving in neutral i'd assume its providing enough fuel and pressure to supply the correct amount of both, however because in gear its not revving properly, i'm to assume it could be several thngs.
I think that its being restricted somewhere,
Fuel
Air
Ignition
Fuel i can suggest here a start may be changing the fuel filter (if your model of pump allows it) and check your fuel lines on top of the pump itself and fuel lines to the engine,
Air, check for vacume leaks (could be at the mani, tb, anywhere) check pipes, tighten and check clips (i replaced the stock ones with jubilee) replace air filter etc.
Ignition can be spark plug tips (clean or replace) coil failure (i think this could be an option) HT corrosion, stock hts are apserlute trash, mine were soiled in corrosion and rust it was horrible, but after a decent sand down and clean up the car felt more happy, responsive, spark contact makes all the difference.
The list with these italian motor diagnostics is tricky, maybe a computer hookup could reveal more, it can be alot of money chasing the wrong thing so its worth trying to fix what you can.
As for limp mode i've not experienced this yet
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