Sorry for my delayed reply. I saw your answer right away, sonic102, but was busy testing.
I've tried setting the object as a container, limited container, closed container, and openable/closeable container. There are no other scripts that open it again. It is in the limo and is visible. It can be closed but not opened, and it starts open.
Here's how I have it configured now:

I have two scripts. One runs when the window is closed, unlocking the room's only exit. That script works. The other is a turn script that says "if the window is open the chauffeur talks to you every turn, else he is silent" but the chauffeur talks every turn regardless of whether the window is open.
Looks like code view has been added to the web interface so here goes!
The first time you close the window (which is currently an openable/closeable container that starts open, cannot be opened, and can be closed) this script runs. I know it succeeds because it displays the message and unlocks the room's only exit:
firsttime {
UnlockExit (limodoor)
msg ("You have closed the privacy window.")
}
otherwise {
}
The turn script evaluates whether the window is open and should display a message accordingly, but only the "window open" message displays, even after the script above succeeds. It's as if the game knows when the window "is now being closed" but doesn't recognize it in subsequent turns as "is closed".
if (not privacy window.isopen) {
msg ("window closed, driver is silent")
}
else {
msg ("window open, driver yammers")
}
Here is the output of a test run:
You are in a limousine.
You can see a privacy window, a door and a chauffeur.
You can go north.
It's fancy.
window open, driver yammers
> look at privacy window
The window is open.
window open, driver yammers
> open privacy window
You can't open it.
window open, driver yammers
> n
That way is locked.
window open, driver yammers
> close privacy window
You have closed the privacy window.
window open, driver yammers
> look at privacy window
The window is open.
window open, driver yammers
> n
You swipe your platinum American Excess through the reader recessed in the car door (no tip) and exit without acknowledging the overfriendly driver. The limo pulls away and you face the restaurant.
You are outside a fancy restaurant.