On the higher HP models of the 15 series, that lever allows you to switch between 540Eco - Neutral - 540.
540 PTO RPM is the standard RPM the most PTO implements run at. If you put it in 540, you 540 PTO RPM at around 2500 engine RPM. There is a mark on the dash for that, usually labeled as PTO 1st.
540Eco, allows you to achieve the same 540 PTO RPM at lower engine RPM, for lighter duty work and with less noise/fuel consumption. Should be labeled on the dash as PTO 2nd.
Anyway, this is more or less irrelevant because you only have 540 available but it was to give some more context to the lever.
Having this lever, that allows you to put the PTO in Neutral is a must. The reason is there is a spring loaded brake that engages every time the PTO is OFF. If you couldn't put the PTO shaft in Neutral, you would have an heck of a time trying to hook up PTO shafts because you couldn't rotate the shafts to align the splines.
Now, for the PTO switch:
OFF = OFF
Manual = On all the time
Auto = PTO turns on are you lower the 3 pt hitch, then turns back off as you raise the 3 pt hitch over a set height. There is a sensor on the upper lift arms that can be adjusted for different heights. EDIT: It will also turn off if you press the clutch on the shuttle shift models.
This is used mostly on low RPM implements like a tiller as those tend to have shorter PTO shafts and raising the 3 pt too high will put those U joints on a very sharp angle.
I don't recommend using this mode with high RPM implements because all of that inertia is very hard on the PTO spring loaded brake and eventually will burn it out.
Lastly, always engage the PTO with the engine at idle. Ideally, turn the PTO off with the engine at idle as well, unless it's some sort of emergency.
I think this cover it all and sorry for the long post.