In a test of the generally accepted Rayleigh-Taylor (R-T) instability mechanism for equatorial spread F (ESF), a linear instability growth rate γRT is derived following the formalism of Haerendel (preprint, 1973) which takes into account the variations of physical parameters along geomagnetic flux tubes. The resulting form of γRT extends the results of previous work by including direct dependencies on transequatorial neutral winds, zonal electric fields, vertical and horizontal ionospheric density gradients, the presence of an E region, and chemical recombination. Realistic atmospheric and ionospheric density model inputs are used for the first time to make quantitative calculations of R-T growth rates for a range of geophysical conditions. The key result of this study is that time/altitude domains having positive calculated instability growth rates are found to coincide with observed time/altitude patterns of ESF occurrence over both a monthly and a yearly time frame. This success in being able to model the climatological occurrence of ESF lends support to the physical model adopted for the instability mechanism and opens up new avenues of research into ESF predictability on a night-to-night and even an hour-to-hour basis.