You are correct, the yellow wire goes to the "S" (Start) connection on the starter. This was because, on the older Vettes, they had "point" type ignition systems, which required 9 volts to run the car. 12 volts would rapidly burn out the contacts on the points.
The yellow wire, when the key was in the Start position, provided temporary 12 volts to the coil for starting the engine, then when the key was returned to Run, the 12 volts went away and the 9 volts continued to run the engine. The way this worked was dependent on the year of your car.
Older engines, like my '65, had 12 volts coming from the ignition switch to a ballast resistor mounted on the firewall which reduced the voltage down to 9 volts, which went to the coil. Later, as with my '68, the ballast resistor, which was not that inexpensive, was replaced with a very inexpensive resistor wire that originated at the firewall electrical block.
So 12 volts went from the ignition switch to the firewall block, then from the firewall block to the coil was a resistor wire to drop the voltage. You could not reduce the length of the wire as this would increase the voltage proportionally and I found you could not with much success solder a standard wire to it due to the type of metal used in the resistor wire. (Ask me how I know
). Also, I'm pretty sure the resistor wire was a solid wire, not strand wire, which made using a crimp connector extremely difficult, as the connector would not hold the solid wire at all.
When the High Energy Ignition System (HEI) came out, the power module in the HEI required a full 12 volts, and the resistor wire went away. In fact, if the distributor did not have a full and solid 12 volts at all times, you would burn up the power module in the HEI distributor.
It is very important to determine which ignition system you have AND
what wiring is in your car.
If you need 9 volts and have the resistor wire, you will most likely be fine with just eliminating the wire. Most all engines I have had started fine on 9 volts, except in very cold weather, which made them harder to start due to a weaker spark and the cold air and fuel temperatures.
In my case, my '65 is running a wiring harness that used the ballast resistor with a HEI distributor. I removed the connectors to the ballast resistor and soldered them together with shrink tubing to provide the 12 volts to the distributor. Then I unwrapped the tape on the harness and removed the wire that went from the starter to the coil and re-wrapped the harness. You could cut the connection and cap it with shrink tubing or just tape over the connector as well.
On my '68, I bought the spade plug that goes into the firewall connector and replaced the entire wire with a standard 16 gauge wire to the distributor to get the 12 volts to the HEI. I have some extra connectors if you need some.
Again, it is most important to determine what voltage your ignition system requires AND what type of wiring is in your harness. Either way, you most likely don't need the wire from the starter to the coil, especially where you live.