Factory Ford electric chokes are designed to operate on 6 volts. The aftermarket Holley chokes, and the Carter/Federal Mogul/Edelbrock carbs are 12 volt units. With the Ford unit, the alternator must be rotating, and outputting current for the choke thermostat to be heated. With the others, the key merely has to be on. In the late '70s, early 80s, GM electric chokes operated through an oil pressure switch. They too were a 12 volt unit.
The Ford alternator can be used in this way because the stator is wound in what is called a Wye configuration. Sometimes called a Star, this style of winding produces higher voltage at lower rpm. The stator terminal on the alternator is the common connection for all three of the stator windings. I won't go into the operation of the alternator at this time, unless requested, but safe to say, at any point in the operation, two windings are connected in series. The midpoint will output one half the total voltage. The initial usage of the stator connection was to supply current to the field relay in the regulator to turn off the warning light. The use as a current source for the choke heater came much later.
Using 12 volts to operate a choke heater designed to operate with 6 volts will greatly shorten its lifespan.
If your single wire alternator stator is wound in Wye/Star configuration, a local rebuilder may be able to set up the alternator with a stator output. If as I suspect, the alternator stator is wound in the other configuration, Delta, then a stator tap is not possible.