what I would do. there's plenty of ways to do this.
get some spade lugs that will fit around the battery posts
crimp to 14 gauge wire, or whatever your sprayer has on its current wiring.
Id run the ground to the back of the tractor somewhere not right next to the fuel filler
and run the positive to a 12v switch that you can get at radio shack - which I'd probably drill a little hole for right near the headlight switch.
run another wire from the other terminal of the switch, of the same gauge back to where you ran the ground wire, and then I'd look around radio shack for a 12v plug - think something along the lines of a trailer wiring plug on your truck (heck, we're pretty much doing the same thing.. )
hook up both to the plug, and then cut the alligator clips off of the sprayer side and wire up to the plug - observing proper polarity of course.
now you have a quick hook up/disconnect for your sprayer trailer and could be used for other applications in the future.