Motorcycle Questions? Ask a Mechanic.
A little more information may be helpful.
Ok, you've got the "good" switch. There were two used and the other was very fragile and the knob was removed in a different way.
Knowing that yours is the good switch and it works with the tool then the problem has got to be in the knob installation. It can be damaged but it isn't nearly as likely to happen with it.
I'm sure since you have the tool you know this but I want to make sure you removed and installed the knob with the switch in the fork lock position. The reason for the long tool is that there are two levels of switching that takes place inside the bore of the switch. Each level controls one of the two power out wires. The bike's circuits are split between these two circuits. The knob is working one of them but not the other.
Is the knob retaining plate locking under the top groove of the cast aluminum "nut"? It sounds like the tip of the knob may not be engaging deep enough down in the switch. You can verify the output on both wires if you have a meter just to be sure what is going on. It may help make sense of the issue.