I've read your last post 5 times now, and I'm still not sure I understand what you are trying to accomplish.
Let's ignore the ladder logic for a moment. Focus on the action-events that you should witness from the mysterious black (or grey) box.
First assumption: The PLC is always powered, and always in Run mode.
Action: Push and hold the button.
Event: After 12 seconds, the output comes on.
Action: Release the button after the output is on.
Event: The output stays on.
If the above is true, I can't figure out how you turn off the output. Is there a second button somewhere?
Action: (With the output off) Press and hold the button for only 6 seconds.
Event: Nothing happens.
Is this what the PLC should be doing? Or something else.
Hint #1: You say that you are using an RTO timer. RTO timers need a RES instruction to clear themselves (although like all timers, they will clear themselves when the PLC is first powered up or put into Run mode.
Hint #2: Here's a typical motor starter ladder:
START STOP MOTOR
---+---| |---+---| |------( )
| |
| MOTOR |
+---| |---+
Does this suggest something?
Hint #3: When posting ladder diagrams, use the HTML tags
[LADDER] before your code and
[/LADDER] after your code. Otherwise, all spacing will be reduced to a single space, and things won't line up