EQ was really vacuum brake's last stand and was Gresham and Craven's answer to the ever present problem of too rapid a reduction in vacuum train pipe levels during braking leading to uneven application along the length of a loose coupled freight train. If air was admitted to the train pipe too rapidly (by the driver at the front of the train) then the actual brake application would be characterised by the rear of the train significantly lagging the front and hence a pair shockwaves would be created as each wagon buffer contacted the next, one at the front of the train progressively moving towards the rear and one from the rear moving forwards which could result in an upward thrust towards the centre of the train where the two waves met and a consequent derailment.
As with all systems at the time there were two braking rates: goods and passenger, and in the former the rate of application was slower than with the latter. In the EQ system this was achieved by significantly slowing the rate of train pipe vacuum reduction, but leading to a more EQual fall in vacuum throughout the length of the train, by a system of chokes to the extent that, for a full application, it took around 30 seconds for the vacuum to be reduced to the required level.
It seemed to be effective enough but some drivers were not happy about the degree of control which was taken out of their hands, in comparison with the judgement that had to be exercised with the products of Westinghouse and Davies and Metcalfe then in use, and the slow overall rate of application. For release the chokes were by-passed by the provision of an electromagnetically activated valve controlled from a push button in the cab and I'll leave it to you to muse over the pros and cons of this as opposed to a sprung loaded position on the actual brake handle.
Probably a good idea technically, and most certianly a serious attempt to correct an ever present danger in the face of increasing train lengths, loadings and speeds, but really too late with the imminent adoption train air braking and the gradual phasing out of vacuum systems from the mid 1960s onwards and, as it transpired, came to be G & C's. last attempt to hold off the inevitable.
There was no need for vacuum EQ provision in dual braked locomotives as the brake application rates (air/vac.-pass./goods) were controlled by the choked reduction in air train pipe pressures on the locomotive, even in vacuum as in either mode the air train pipe on the locomotive was the governing medium; i.e. on air braked trains the locomotive air brake pipe was coupled directly to the train air brake pipe and in vacuum the same air brake pipe governed the level of vacuum in the vacuum train pipe through the Air Vacuum Relay Valve on dual fitted locomotives.
I recall no specific workings for which EQ fitted locomotives were diagrammed although that is not to say that this wasn't the case or that there was not any particular working for which a locomotive so provided was not preferable although, from my recollection, it was just another method of control which could be universally applied throughout the system.
I hope that this helps, D7666; I must have missed your original posting, the date of which corresponded with the death of my hard drive.