The green white wire is what we call a signal or trigger wire.
It is not a current carrying wire which is why it is so thin.
If you have a remote solenoid make sure it has a good ground as it grounds out through the body, unless there is another small wire , which is the ground.
Next make sure the starter has a good ground.
I like running a jump start jumper from the battery - to a good ground spot near the starter like the lifting lug or the drain plug