That might work on a Harley or a model with separate indicators, not going to work on a Honda without extensive rewiring, if at all. If you note the key down below the wiring, the Honda switch has 6 wires and is 2 single pole, double throw switches internally. yours seems to have only 1 single-pole double throw switch. When you move the Honda switch left or right, it opens up the front run light for that side so the light goes on/off rather than bright-dim. the other half routes power to the turn signals. Also note the indicator on the Honda runs to both sides, and counts on grounding through the non-blinking side's bulb filament. Not a problem with the incandescent as you drop most of the current through the indicator bulb filament.
LED lights are another matter. Did you use LEDs? You can fix the crossover blinking on them by rewiring the indicator and adding 2 diodes. (most any diode rated for more than 12v and 1 amp, a 1N4002 would be fine and plenty heavy duty enough) Just add a diode to each indicator wire and tie both negative ends of the diodes (silver band) to the same indicator terminal. then ground the other side of the indicator. the diodes act as one way check valves and prevent the crossover. The lights can also backfeed through the run side of certain LED lights and the oem lights Might need a diode at each turn signal light input to prevent the run light from backfeeding, not sure if this will help yours as the switch you have doesn't appear to open up the run side.
To find out, unplug your indicator bulb, see if the turn signals work.
Also note the Honda switch is rather unique in that in the neutral/center position, the PR/PL side has power to all 3 contacts, and opens up whichever side you move it to. Never seen an aftermarket switch that works that way. Only fix I see to use your new switch would be to disable the parking lights in front by not connecting the light blue/white and orange-white wires. And if you used LED lights, to rewire the indicator with diodes.
gray is power in from the flasher, lt blue is right turn, orange is left turn
When we say indicator, we mean the little light in the dash, I noticed some other countries call the actual turn signal light assembly the "indicator" just clarifying. And LEDs are also diodes themselves, so are polarity sensitive. If they don't light, try reversing the leads.