I have the same handle on my 4110, it's the same one used on the 110TLB's and it IS a switch on mine-it operates my horn.\
Here is an older post: http://www.tractorbynet.com/forums/customization/110476-joystick-handle-horn-install.html
You can purchase just the membrane part of the switch through JDP.
Thanks Kenny! I did try searching the forum, but somehow missed out on your excellent post.
I wonder if it is a switch on my 4720? I didn't tear it apart, but it feels "hollow" under the little square.... You don't feel a "click" when you press it, like when you press the 3rd function rocker switch. It would be the ticket for the diverter.
What would be really cool, is rigging up a "flip-flop" relay... Press the button once to latch the diverter on.... Press it again to unlatch it. That might work good for controlling things behind you.
That is a great idea! Funny -- I haven't even got my tractor yet and I'm already thinking up mods.