After watching a video on AppliancePartsPROs.co and inspecting my agitator, I came to realize that the splines of said agitator, which engage with the exposed shaft of the clutch/drive assembly, had, after 13 years of use, worn away.
I ordered a new agitator (pulsator) from AppliancePartsPROs.com along with a new bearing washer. The parts were delivered by FedX within two days.
I had already removed the original pulsator and plastic cap. I aligned the pulsator splines with the drive bearing shaft and once engaged, tightened the included screw with a 10mm socket wrench. I snapped the plastic cap back on and then tested for function.
Installation took all of ten minutes. My wife was very happy.