It never needed a battery to run. The Briggs engine has a flywheel magneto - regardless if pull start or electric start.
If you ever have to change the ignition switch, you have to make sure it's a switch made for flywheel magneto and NOT battery igniton. With a mag switch - ON does nothing and OFF shorts out the magneto. With a battery-switch, ON sends power to the coil and OFF stops the power.
Starter generator needs a battery, voltage regulator, high-amp push button for starting, etc.
Many of the tractors got the electric start added at the dealership. I had to do many (I worked for Bolens dealer in the 60s).