Alright, I checked the combinations with the multimeter, and the combinations that had a reading in each position were:
OFF: green - white/black
ON: black-red
OK, to start with you will have a reading on your ohm meter when you touch the leads to any 2 of of the wires from the switch. If the switch is clean & working perfectly (as a brand new one should be) the reading will be either zero ohms or infinite ohms. Depending on your meter the indication for infinite ohms will vary but it will generally be the same as when the leads are not connected to anything (this is why I directed you to the Electronics Club to learn how to use your meter).
So what i think you mean is:
the green and black/white from the new switch are shorted when it is OFF and open when it is ON (& not connected to either of the other wires ever - I forgot to mention that
) and
the black and red wires from the new switch are open when is OFF and shorted when it is ON (& not connected to either of the other wires ever)
Which is what I expected you would find. That's good. It tells me that this switch is not really "universal" but was made for a Honda because the wire colours match Honda's standards (other manufacturers use the same colours for different purposes).
(Note that I specifically said black/white instead of white/black as you did. The identical part that I have here matches the pic in the Amazon listing where you bought it and that shows a black wire with a white stripe, not white with a black stripe. This may not seem significant right now but when you progress to other parts of the bike's electric system you may find that there are 2 wires with opposite main colour/stripe colour and it will be easier to deal with that if you develop good habits now.)
To understand what is going on here imagine that there are 2 separate switches inside the keyswitch assembly, arranged so that when you turn the key one way one of the switches (lets call it "A") is on and the other switch ("B") is off and when you turn the key the other way A is off and B is on.
I have a feeling that the schematic seems overwhelming to you but it really isn't that difficult to figure out if you take it one part at a time. In the upper right you will see something that looks like the pic below. It is a representation of what goes on inside the original keyswitch when you turn the key to the various positions, as indicated on the right.
Starting from the top, when the key is OFF the green and black/white wires are connected together and none of the others are connected to anything. This matches your new switch so you can connect the matching colours.
Next, when the key is ON the red and black are connected together and the brown/white and brown are connected together. The red is power from the battery and the black is the wire that carries power to just about everything on the bike, either directly or through a fuse or switch or something like that. This means that the red and black are connected to a part of the original switch that matches your new switch so you can connect them to the matching colours too.
The last position of the original switch (PARK) is for the parking lights. In some parts of the world you are required to leave lights on at the front & rear of a vehicle when it is parked on an unlit road but that is not required in North America so your new switch that doesn't have it will still be legal. If you were to follow them back through the wiring you would find that the brown wire takes power to the tail light and the brown/white wire goes back to the fuses and some other stuff like instrument lights. That other stuff doesn't have to be on with the parking lights so the switch is set up to connect the tail light (brown) directly to the battery (red) when the key is in the PARK position.
As I said before, you don't need that, but you do need to get power to the tail light when the key is ON. If you connect the brown/white and the brown together your tail light will get power from the same place it does when the old switch was ON and will work normally.
I know this seems like a long way to tell you to connect the wires from you new switch to the matching colour wires that went to the old one and connect the other 2 together but my goal is to teach you how it figure it out yourself the next time.