UPDATE:

I removed the resistor and examined the wiring. There are no obvious problems. The wiring harness at the blower resistor connection looks good.

There are 4 positions on the fan switch. With the blower resistor removed, the fan will still run on high speed. There are 3 wires that go from the fan switch to the blower resistor. With the switch on low speed, there is 9.6 volts in one wire. The next faster speed has 9.6 volts on 2 wires. On the 3rd fastest position, there is 9.6 volts on all three wires. Is the 9.6 volts the problem?

On the resistor, I used an ohm meter to test between the various terminals where the wires connect to the resistor. There was virtually no resistance on any of the circuits. Several of the circuits had 0 ohms. A couple read less than 1 ohm. In looking at the resistor, I don't understand how this outcome can occur. It seems like it should either have some resistance or else be an open circuit if the resistor is burned out. Maybe I' do not understand how the resistor functions or I'm not testing it correctly?

Any advice?