Hi Dipper, I also have a JD LT 445, a couple things i guess you know, if you have just been in reverce the PTO will not come on if you try to turn it on before moving foward just a bit, also if you are mowing and go to back up the PTO will kick out, You can pervent this by Lifting up on the switch as you start to back up, just lift it up and release it while you are backing up & as long as you are backing up the PTO will stay on, I am sure you know all this,
If the switch keeps acting up I think it is the switch & not the Elect Clutch, I haven't looked at the switch from the back side, I would think that there should just be 2 wires, I think you could test it by just taking a heavy duty toggle switch and hook it up in place of the push pull switch & see if it works right, if it does you know what to do