how can I wire x300 john deere to mow backward without holding switch up?

If this is what you want to do then look at the switch on the bottom side. On older models there are two wires. Newer models have three wires. Simply wire both or all three together and the switch will be disabled and you can mow in either direction. You can put it back if you desire.

John Deere X300 Wiring Diagram

You can't, this is only for safety reasons. What happens if you hit a dip in the grass, or fall off the edge, all because you didn't see it. Or hit, throw a rock at someone that you didn't see. You can still cut going backwards IF you hold the PTO switch up. NONE of the John Deere models are able to mow backwards. Not even the zero turn models.

Safety First...Good Luck!

You will need the wiring diagram. Take a look at what wires need to be connected to disable the switch. It may be as simple as disconnecting th wires from the switch and connecting them together.