Mitsubishi alternator, T-shaped connector:  The cross-bar of
the T ("R" terminal) must have battery voltage applied in order to
build up a magnetic field in the rotor.
    The upright of the T ("L" terminal) is used to operate the
charging indicator lamp.  It does not have to be used in order for the
alternator to function.
    The large insulated stud terminal is the main positive
charging output to the battery.
    If there is a single 1/4" blade terminal by itself, separate
from the R and L terminals, it's connected to the alternating current
induced in the stator, before rectification.  The AC signal can be
used to drive a tachometer or other speed sensing device.
    The common ground (battery negative) is through the die-cast
case.  Connection made by the mounting pivot bolt to engine block,
timing cover, etc.

The most important part of a cold start is the choke, second is a good
spark, (having a new distributor cap and rotor once a year is a god
thing) and third is a good gas supply.  A plugged gas filter can cause
cold start issues, a gas filter with two outlets (return line) if not
turned the right way up can cause the gas to syphon back to the tank
when it sits causing really long starting cranks.

It would help if you gave a a clue to the vehicle.....

Mike
86/00 CJ7 Laredo, 33x9.5 BFG Muds, 'glass nose to tail in '00
88 Cherokee 235 BFG AT's