OK, at least some of the scoop on P-L-F-S. From this excellent web page:
Alternator Theory v15:
"The terminals are designated as follows:
P-Terminal: The Pulse/Phase terminal can provide a 12V square wave to determine alternator speed, used by some Electronic Control Units. Connects to the stator. Some ECU’s monitor this signal and adjust engine parameters accordingly.
L-Terminal: This terminal is connected to the “Low” side of the warning lamp, with the lamp’s “High” side being fed by the ignition circuit. Some regulators require a 35-ohm resistance inline with this circuit if no lamp is used otherwise alternator damage may ensue. Some applications have a resistor connected in parallel to the lamp in case the lamp bulb opens up and burns out. The resistor will be there to provide a path for current and voltage. Some vehicles supply a 5Vdc reference to this terminal from their ECU; other vehicles don’t, so be aware of the various models of regulators. Other regulators may be tested by application of a 50-Ohm pull-up resistor to connect the L-Terminal to the 12Vdc source, I believe that any resistance between 35 Ohms (5-Watt resistor) and 500 Ohms (1/2 Watt resistor) can be used safely.
F/I-terminal: has several duties depending on the specific regulator, some regulators have a resistor that is internally connected between the Field and Lamp terminal. Other regulators use the F/I terminal to provide field duty cycle information to the vehicle's ECU. These regulators are not interchangeable, but for our Jeeps, it hardly matters. For ECU related vehicles it can be of paramount importance. If the alternator that is selected comes from a vehicle that only uses the I-Terminal then the wiring may simply require a wire from an ignition source in order for the alternator to operate correctly.
S-terminal: This is the “Sense” terminal and is connected to the battery. It senses the voltage level of the battery and feeds the regulator circuit this reference so that the regulator can adjust the Pulse Width Modulation to control the alternators output. The S-terminal on the CS-130D regulator is the same size as the other three terminals, unlike that of the CS-130."
So, Cam, it sounds to me like F and P connections are not needed for your application.
EDIT: For sure the P terminal can be left disconnected. After more reading the F/I terminal may need to go to switched 12v power through a fuse. I say "may need to go" because it looks like there are different models of these alternators out there. Did yours come with the LS motor and do you know what vehicle it came out of?