The clicking you hear is the starter solenoid. It is located under the seat.
I circled the solenoid, and the arrow point to where it is located. You will probably have to remove either the battery, or the fenders to get to it.
solenoid.jpg
You need to check the solenoid for loose wires/ bad connections. They do fail, and usually are a universal type and can be picked up at most parts stores for under $20. Good thing to try as it is a lot cheaper than a starter.
More places to look for bad connections:
*Trace the ground wire from the battery to where it bolts to the frame. Clean this point with sandpaper.
*Check the connections at the solenoid. Look for wires that appear to have been hot. They will be discolored.
*Check the connection at the starter.
#1 Problem with these machines is they really don't have heavy enough wire from : Battery (-) to the frame, and it actually should run to the motor; and from Battery (+) to solenoid, and from solenoid to the starter. I personally think that is why the starters don't seem to last long. However, I am not suggesting you replace them with larger wire, unless they look damaged. But, if replacement is necessary, I would use the next size gauge wire.
It is very possible that the starter is starting to fail. There really isn't a very good test for this. At least not without some special tools.
One thing you can do, as a test for the parts of the system between the battery and starter is to get your jumper cables, hook one end to the cables to the battery, and the other end to the motor like this. (see pic) LISTEN CAREFULLY: Disconnect the battery wires first!! Hook one end of the cables to the battery first, then attach the other end of the Positive jumper cable wire to the post where the RED wire is attached to the starter. MAKE SURE IT IS ONLY TOUCHING THE POST AND NOT THE STARTER BODY! It will SPARK if it touches the body!!! Then, open the jaws of the negative and grab the spot of the motor in the pic. IT WILL START CRANKING! and will continue to until you disconnect. This bypasses all circuits! If the motor cranks fine, you have wiring issues. If it doesn't, you either have a weak battery, or a bad starter. Charge battery and try again. Do this ONLY as a last test before replacing the starter!!
right side of engine.jpg
Some things to be aware of while working on any machine:
*Don't crank the starter for more than about 15-20 seconds.
*Since your starter on this machine is easy to reach, carefully touch it if you have been cranking a while on it. If it gets hot, STOP, and let it cool. You can "burn" it up.
* If the motor doesn't fire after 2 or 3 15 second cranks...... It's probably not going to start. Keep looking for the problem.
*Don't run the engine very long with the top cover off of it. The motor will overheat. 1-2 min is long enough!