Total amount of time: 10 minutes!
Install instructions for future searches on this issue...
Oil sender replacement for the W124 M104-series engine.
Step one: Jack up driver's side of vehicle.
Step two: Remove air deflector shroud underneath engine.
Step three: disconnect sender lead from sender (may take a flat-blade screwdriver to do this since there is miniscule room for leverage to pull it from the fitting).
Step four: Unscrew the sender using a 17mm wrench. Preferably, a short one...there is little room for untightening (or tightening). Fortunately, one or two twists will allow you to loosen it by hand.
Guess what? Not a drop of oil dripped (or poured) out! Perhaps jacking the car forced the oil to the passenger side of the car. Or maybe the fact that I didn't drive the car for a day (it's been SL weather lately

).
Step five: Screw the new oil sender back in. This is the hardest part of the job, because the tight confines require a bit of trial-and-error on sender thread orientation. Eventually, it will hand screw right in and a couple of twists with the wrench seats it.
Step six: Reattach the sender wire.
Steps seven and eight: Reinstall the air deflector shroud and lower the car down from the jack.
The gauge needle no longer pegs to "3" when I turn the key (without cranking the engine). A test drive confirms that the gauge now operates as it should.
Thanks to all for coaxing me through a task that I had procrastinated on for nearly three weeks!