It cannot be done with the existing wiring.

What you have is know as a switch loop. There is no neutral present in this box.

"2) because the wires running into this switch aren't white, black, or red...they are old and covered with cloth. "

If you look closely at the cloth covering it is colored.

Look back near were the conductors enter the box.
Cleaning the conductors (A vacuum works well) can also help reveal their color.

Many of the older cloth covered conductors use rubber insulation. This insulation can be very brittle and can fracture when the wires are moved.
Sometimes the cloth layer holds it in place despite the fracturing.

Heat shrink tubing can be applied over both bare wires and fractured insulation to restore insulation integrity.