Both coils on it now have an "L" printed on the coil wire, one has an orange paint dot on the coil body, the other a blue paint dot, and both have the same length coil wire. One looks newer than the other.
The old (although it looks new) coil has an "R" printed on the coil wire, an orange paint dot on the coil body and a small blue paint dot where the diode wire plugs in, and the coil wire is shorter than the other two (obviously for the right side). It was in the bag that I received the new coil in, Honda part # 30500-ZJ1-845; I wonder if the bag had the wrong coil in it. I managed to lose the receipt but highly doubt I ordered two coils - that wouldn't be normal for me.
I started working on this last fall and have switched the two "L" coils around so many times that it isn't funny - I don't remember which is supposed to be the new one. What really confuses me now is that I've been getting spark on the right side only but with both coils marked with the "L" on the coil wire, never any spark on the left side of the engine no matter which of those two coils are installed there. The mower runs smooth on one cylinder but obviously has barely enough power to very slowly cut grass, in addition to dumping gas past the rings and into the crankcase. (I've installed a low psi electric fuel pump to take the pulse pump out of the loop on that problem, just in case, even though the pulse hose was dry.)
I'm going to go out, put the "R" coil on the right side and the a "L" coil on the left and see what happens....
Again, THANKS for the help - I usually ain't this dense!