I think the spec sheet (haven't looked at it for a while) gives a maximum voltage for the control pin.
The zener has a sharp turn on conduction curve. Very high resistance (not open) below the zener point, and a dynamic resistance above that point. Find a representative conduction curve via Google.
The specs you would be interested in would be:
Zener voltage, at 1ma, zener voltage at rated power level, the power level (like 0.5 watts @ rated forward voltage).
Reverse voltage for the zener diode should be higher than the expected maximum voltage (like 20 volts reverse rated).
The current/ power consumed by the zener would depend on the pull down resistor on the OKR control pin.
The resistor should be such that the OFF voltage is below the 0.4 volts in the OKR specs. The on voltage should rise to over the spec sheet ON voltage.
There will be a compromise because of the 'undefined zone of operation' at the control pin. 6.4 volts at the positive input, 6 volt zener, 0.4 volts at the control pin (with a pull down resistor) seems like it would cut off. 6.6 volts at the positive and it MAY cutoff, 6.6 volts and it MAY cut off. 7 volts and it will most likely stay on, 7.4 volts at the positive and it will stay on for sure.
Switching in this 'undefined zone' may be different when going from an ON to an OFF state, than when going from an OFF to an ON state.
I don't think we want a 'works most of the time' situation.