Your 560 is very likely suffering from the common Red Iron ailment of a worn shift lever. To make sure, take out the three cap screws at the bottom of the shifter tower and lift the shifter out. What you will see are three shift rails, (approx 3/8 wide) and two dividers (approx 1/16 inch wide) with about a 5/8 slot in them. To have the transmission in neutral, all the slots must line up. With the shifter or a large screwdriver or other pry bar move the rails until the notches line up with the dividers. You may need to depress the clutch, pull the TA lever, and rock the tractor back and forth to accomplish this. After aligning them, you can put the shifter back in (make sure that the bottom of the shifter lever goes into a notch. BUT before you do this, take a good look at the bottom of the shifter and determine how much it is worn. I usually build mine up plenty, then grind them back down until they just barely fit and work, that way it will be a long time until this problem occurs again.
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