The cloth covered wire is the ignition wire from the key switch to the coil (OEM)
It comes into the cab through the firewall terminal block behind the fuse panel and becomes a pink wire which runs to the key switch after teeing with two other pink wires as shown in the first diagram and then the second.
The green wire is the temperature sending wire which goes to the key switch if you have the idiot light dash, and then to the dash cluster to the no. 5 pin on the cluster plug. If you do not have the idiot light dash but have the gauge dash then the green wire goes to pin 6 on the cluster plug and then to the temperature gauge in the dash. It sounds like this wire may be shorted to a hot wire at some point since it is grounded through the sender to the engine block.
Look at the two diagrams and on the lower left you will notice the firewall block and the pink ignition wire coming out of it in the top section. Follow this wire up to the tee and on up it turns right and heads to the ignition switch.
Just to the left of it is the green wire for the temperature sender. and below it in the second diagram. Again this wire goes to the dash cluster plug if you have a gauge dash.
Ignore the arrows, they point to the brown accessory wire which goes back to the fuse panel to power the turn signal flasher, the wiper switch and the hazard flasher.