Investigation:
Disconnected dryer and removed back panels console upper and back plate and opened up top panel to access dryer door switch. All open panel trouble shooting performed with room closed off to other people, children, and a curious cat along with disconnecting the dryer during troubleshooting.

1. Jumped (connected) the door switch pins and no difference. Dryer would not start. Tested door switch with a multimeter and confirmed it was locked in the door closed (dryer on) position.

2. Removed thermal fuse on exhaust and tested with multi-meter. Showed as blown / broken so 196 degrees was exceeded. Most likely during that last use the temperature was just under the fuse breaking temperature while the dryer was running and intaking cool air but after shut off the temperature spiked over the 196 degrees and broke the fuse.

3. Jumped the thermal fuse connectors and dryer was able to be started and would run. However, timer still exhibited same faint buzzing sound. And now the heater ran on all four timer selections including "No Heat Fluff". Wife confirmed that "No Heat Fluff" was never supposed to heat even to low levels.

4. Researched Appliance Parts Pros forums for similar issues. Found most likely cause would be heater coils grounding out to chassis. This often would be caused by lint build up on the coils grounding out the coils.

5. Pulled the coil out and found that the coil section that connected between the "back" and "front" of the coil panel had shifted down because the ceramic support at that point had worn down within the metal frame. I was able to revise the coil at that point by pulling the coil off the ceramic support and re-positioning it to better tension the ceramic support in its hole in the metal panel. After doing this, tested the dryer and the heater functioned correct on all cycles and the timer no longer had the faint humming or buzzing sound. The faint humming or buzzing sound was apparently the timer being energized by the grounded coil shorting electricity to the timer.