Ill try draw the logic board now

[S.off] [S.on] [ B ] >this button triggers both top (AND)(AND) switches and both AND gates >link each switch to the AND below it

[ T ] [ T ] >The left AND gate from above (ANY) (ANY) will trigger both the piston's ANY [S.off] [S.on] gate and the rotor's delay gate (Seq) (seq) (which links to the rotor's ANY Gate). Link the top right AND gate
to the rotor's ANY gate and the piston's delay gate. When the Button is pressed a second time, the system will reverse

Rotor | piston