My 2001 425 AWS has had a very sensitive reverse safety switch for a long time. I have to actually be rolling forward to get the PTO to engage and stay engaged without pulling the knob all the way up. This weekend, the PTO wouldn't engage at all and I suspected the reverse safety switch that I learned on this site is named the RIO switch. Mine is on the inside of the right frame rail, mounted on top of the bottom flange. It is a grey, button type switch. The brake switch looks the same and is on the left frame.
The easiest thing to check was the seat switch. I disconnected the seat switch and installed a jumper wire in the connector but the PTO still didn't engage.
Since my PTO engaged light on the dash wasn't working either, I thought the trouble must be in powering the circuit, not with the PTO itself, but I checked the PTO solenoid coil anyway. I disconnected the PTO solenoid coil located on the back of the transmission near the top and supplied 12 volts to it to hear it click. That told me the PTO solenoid itself was good.
The RIO switch wasn't easy to find. Not wanting to remove the mower deck which I find difficult, I removed the seat, rear fenders and gas tank. By fiddling with the pedals, I finally located the RIO switch on the top of the lower right frame rail. Nothing came close to contacting that button switch. Then I discovered a relatively thin metal strap that was hanging loose from a mechanism tied to the forward-reverse mechanism. I swung that strap forward to see that it had a shinny place where it used to contact the RIO switch. I disconnected the RIO switch and installed a jumper in the connector. With the jumper still in the seat switch and a jumper in the RIO switch, I made sure the brake was not engaged, turned the ignition to ON and pulled the PTO knob. The solenoid clicked to confirm it was the RIO switch that was the problem, or actually the mechanism that is supposed to engage the RIO switch. I tied the jumpered connector to the RIO switch up to another wire to keep it from dangling and getting caught on something. I reinstalled the tank, fenders and seat, reconnected seat switch and everything's working fine. Plus the PTO won't turn off when I back up a foot to avoid an obstacle.
This fall when I take the mower deck off for the winter, I'll be able to access the mechanism that is supposed to depress the RIO switch button to see what's wrong and decide to fix it or leave the RIO switch out of the circuit.