This is driving me a bit crazy. I'm using a Nikon Z6 with the 24-70 F4. I cannot access the interval timer shooting menu (nor the time-lapse movie or focus shift shooting); the camera insists "This option is not available at current settings or in the cameras current state". It remains greyed out. Yet I have tried all the settings I can think of, RAW, jpeg, manual focus, shooting in video mode, a variety of release modes... nothing will make it accessible.
I experienced a similar problem, the "Time-Lapse movie" was grayed out and could not be used. Turn out to be the XQD memory card was not in the camera slot. Time-lapse can only be activated if the XQD card is well inserted in the Z6 Camera.