Here's where you find the two wires you need.

Take the side plastics off the bike. Look down at the lower left aspect of the radiator (meaning the rider's left).

Here's a closeup.

You should see the fan thermo-switch (here brown colored), with two wires coming out of it. One wire is hot when the ignition is on, the other is ground (black wire). On my bike, as you see, the hot wire is yellow, not orange as the repair manual's wiring diagram would indicate. And although the ground wire appears brown in this photo, it is in fact black, as it should be.

These wires do not power the fan directly. But when their circuit is closed by the thermoswitch at 221°F, they activate the fan motor relay, which relays current flow to the fan motor.

So if you want the fan to go on, just make contact between these two wires shown(with the ignition switch on) and the fan should come on. To have your own manual fan motor switch, you can follow these two wires along the left side of the bike, and tap into them at any spot you like, then just insert a simple SPST switch and you're done. Mount the switch wherever it is convenient.

Some riders have wanted instead to attack this problem at the site of the fan motor relay itself. If you wish to do that, you can find the fan motor relay under the seat, just in front of the battery, on the right. Don't put a switch on the fuel pump relay by mistake!!! See photo below.

Note the location of these important parts: TO sensor, fuel pump relay, and the fan motor relay.

The tip-over sensor (TO Sensor) is very important. If the bike leans more than 43 degrees, this will shut off all ignition spark and fuel flow. Sometimes people remove this while making other repairs , and then re-insert it upside-down. If you do that the bike won't start.

Also, the location of this sensor makes it vulnerable to injury when a rider drills to insert a TRE switch or other switch. So when you're drilling, be careful! You never know what you might hit on the other side of that thin plastic.

Here is the wiring diagram to explain what you are accomplishing by inserting your switch by the first method (at the radiator).

Realize that on the GSX-R, all orange wires (regardless of whether they have any colored stripe or not) are HOT whenever the ignition key is turned ON. So when the ORANGE wire is continuous with the BLACK wire, the fan switch relay will be activated, because this current from the O wire is transferred to the B wire, which powers the fan motor relay coil. You can see that the relay coil already has a ground connection (B/W wire). When this relay coil is activated, the standing current in the O/R wire at the fan motor relay is now connected to the B/R wire exiting the relay, so that the B/R wire is now HOT.