can't really see the cam profiles in the pics, and don't know if the panel is open or closed. I'm guessing the panel is closed.
the cam closest to the motor is the A cam. If the switch on that cam is closed, the shuffle motor runs. If the gate relay or start relay is powered, the shuffle motor also runs. The A cam should have 2 notches ... one at panel fully open, one at fully closed.
here's probably the sequence when the shuffle panel is closed to reset the game:
1] close the coin switch, the start relay powers. With the panel closed, the cam B switch with the blue/red wire is closed, so the start relay stays powered.
that turns on the shuffle motor via the start relay switch (and more importantly, keeps the motor power on until after the A switch has closed), and another start relay switch causes the lock relay to power. The lock relay should stay powered forever unless the game is tilted or the power is turned off. If your lock relay is not working, then you should disable the switch on it that powers the gate relay, otherwise when the panel reaches full open the gate relay will power and keep the motor going. The side effect is if you turn the game on or tilt it with the panel open, it won't slide closed. That may effect something else, so you might need to fix the lock relay if it's not right.
2] shortly after the shuffle cams start turning, the A cam switch closes and now the motor is powered via two parallel/redundant circuits.
3] as the shuffle cams spin, the cam B switch opens and the start relay loses power. The motor keeps going because the A switch is closed.
4] when the panel reaches full open position, the A switch opens and the shuffle motor turns off.
the C switch should now be closed, so when the gate switch is triggered by the ball, the gate relay will power and turn on the shuffle motor to close the panel.
you should be able to manually turn the shuffle cams and see the switches doing their thing. If they are opening/closing as makes sense for the profile, then I'd guess the issue is gate relay powering when it shouldn't ... lock relay switch stuck closed, lock relay not working or the gate switch is stuck closed.