Motor reverser with limit switches

I am building a reversing target that will use a 12vdc motor. The idea is to have two steel plates, where hitting either plate will reverse the motor direction. If the motion is left, hitting the left plate will reverse the direction. Motion right, hitting the right plate will reverse the direction. The plate assembly will include the motor, battery, plates and electronics. If the assembly moves to the extreme right or left, a limit switch will stop the movement. If the movement stops left, hitting the right plate will reverse motor direction, and start the game again. You win, if the assembly stops on your opponants limit switch. Or, if shooting the target solo, the idea would be to keep the assembly moving right-left without hitting a limit switch.

I have this link to a Motor Reverser w/limit switches form Electro-tech-online. I think this would work for me, if I could figure out how to use two direction switches activated by individual steel plates.

https://www.electro-tech-online.com/attachments/motorlimitswtreverser-gif.22122/

Thanks for any assistance,

Wayne in Montana