That’s right, none of the persistence services store UNDEF (or NULL) by design.
That’s right, that is just what restore-on-startup is intended to do. Maybe you don’t want old values restored at boot, that’s a persistence configuration issue.
You’ll want the displayState here (coupled with MAP in your Item metadata ‘pattern’).
What’s in your secret MAP file?
I don’t think a MAP will deliver what you want though, if you don’t know all the other possible values in advance.
This might help