If for some reason you want to have mono when the cable is plugged only into the Left (mono) jack, but stereo if both cables are present, you can do this with the style of jack that grounds the sleeve to the ring when a cable is inserted.
You put a resistor in series with both outputs (say, 1k), then connect a resistor between right sleeve and tip, then connect the sleeve through a resistor to the left tip.
If the right channel jack is unplugged, then there is a path between right tip to right sleeve to left tip. The combination of resistors from both ends should be equal to get 50% R/L mix at the output.
Then if you plug a cable into the right jack, the junction between the two tips gets shorted to ground when the plug shorts ring to sleeve. Both outputs are at 1/2 volume, but not mixing together since the mixing junction is grounded.
As for the way I do it, I process the left and right channels independently so I have 2 series mono processing chains. Then I use channel 1 for pre-distortion effects (wah, EQ, compressor) and channel 2 for time-based effects (delay, phase, flange, reverb, etc). Then I have a pre-processing loop and a send/return loop for distortion pedals.