The origins
A bit of historical perspective from my looking glass. While I am sure it is debatable where the term double tap came from I can only tell you what I know. The lienage as I know it came from the Brits' SAS teams who would use the technique to describe the number of shots fired on a tango.
At this point in history sights really were not a part of the equation, it was implied they were used to put the rounds on board. When our AT teams stood up they were modeled after the SAS models and along came the verbage.
The double tap was a means to engage a threat in your field of fire during your primary sweep. Upon encountering the threat, it was 2 shots in rapid succession on the threat and then transitioning to the next threat. Remember that these were dynamic entries and with overlapping fields of fire the threat was getting hit by multiple team member on both the primary and secondary sweap so you do the math.
It evovled into today's hammer or accelerated pair, but it didn't start there. I was first exposed to the double tap from an exchange offier doing a one year tour with our AT teams back in the 80's. In addition, the term double tap was removed from all documentation at NSWC in 1996 to adhere to a more politically correct scene and we argued vehemnetly against it, but it was enevitable. While we still used the term it was retired in place of other verbage. And lastly, when taught the technique really didn't center around the sights, but the results. It was implied that one would use the sights to fire the two shots. Also remember that the primary weapon system was the MP-5 where firing two shots quickly on target really was a matter of how fast the shooter could pull the trigger and not re-aquire the sights. When we shifted over to the pistol there was difficulty for some due to the reliance on the primary weapon system's quick recovery.
The bottom line, it has evolved quite a bit over the years and it assimilated itself into the hammer an accelerated pair crowd, but that is not where it started. I can only tell you what I know, what was passed down to me.
Later,