@Junior posted:...
Sorry about confusing negative with ground. It's easy to forget that AC and DC are two different animals.
"By "negative side" of the circuit I believe you're referring to the lamp connection to the switch frame which is hooked up to the outer-rail or train transformer common." Yes.
"So getting back to the matter at hand, the external diode only passes positive voltage pulses to the LED
"+" terminal, so this terminal is always more positive than the LED "-" terminal (case)." This is where I'm not getting it. I understand what the diode is doing; blocking the negative pulses from the AC coming in. But in this case, what completes the circuit to the LED; allowing it to light up? Is it the connection to the switches Common? Does this "work" because the diode is blocking the negative pulses on the positive side of the LED; which allows only negative pulses from Common on the negative side of the LED?
Never a teacher...but of the school-of-thought that a picture is worth a thousand words. 
Right. It is the connection from the LED case to common that completes the circuit allowing the train transformer AC to power the LED. And the diode insures that the LED "+" terminal only sees positive pulses. A positive pulse or voltage is "positive" with respect to, or relative to, a reference. In other words the voltage represents the difference between two points in the circuit; the difference can be positive or negative. In this case that reference point is the common bus or outer-rail. It is expedient for analysis purposes to think of the common as being 0 Volts or the horizontal line on the graph.
It is indeed confusing that the reference connection might be called "common" or "ground" or "neutral" or "return" or "black" or "zero" or "outer-rail".
Keep asking questions!
BTW. I have been consciously avoiding "current" or Amps in the discussion. Voltage and current are as thick-as-thieves as it gets! But I believe the issue at hand (your dying LED bulbs) can be satisfactorily explained using voltage only. 
