An odd question but where does the cable from the auto shifter go to and what does it do?

it goes from the top of your auto through the fire wall to the hand seletor. when u move the hand seletor up and down it pulls the shifter cable to tell the gearbox what gear u want it in eg. drive, reverse etc etc

Would there be another way to tell the gearbox what gear to go into, EG electronically?

Might be possible, but would not be an easy task to do. Would require a fair bit of mechanical and electrical know-how to do I would think. Many modern cars don't even use that sort of method!

Would there be another way to tell the gearbox what gear to go into, EG electronically?

not as such... the automatic shifter cable directly moves the manual valve in the valve body of the the automatic... also the park brake it activated manually. 'L' with the shifter is different than first in 'D' also.

you can control what gear it's in when in drive using the solenoids.