Not specific to the Zephyr, I have found intermittent crank issues to usually be due to a faulty solenoid contact in the starter/solenoid assembly. The battery voltage and terminal connections are good but the solenoid just 'clicks' when trying to start the car instead of engaging the starter and cranking the engine like it should.
My '96 Mark VIII currently exhibits similar symptoms but will crank right up once a battery booster is attached. My guess is the extra juice fires across the solenoid contacts easier?