Since all of the wiring in the engine compartment and behind the dashboard was turned to charcoal, I figured the easiest way to replace this wire would be to remove the dashboard. Surprise! The dashboard is not removable--it's an integral part of the car body. Nonetheless, this was a good opportunity to get things out of the way, so I could start replacing the wiring behind the dashboard.
A closer look at the instruments shows that they are a total loss and will have to be replaced.
1954 Chevy Dashboard
1954 Chevy instruments