I was also taught “1000-2000” and, whilst I don’t have a 100% start rate, my unscientific gut feeling is that it gives a slightly higher success rate than those who don’t pause.
I have no doubt that the APU start switch is simply a switch and the pause can’t be shown to help on paper, in much the same way that the engine start levers are switches and should not be used like a mixture control. My theory for its success is that you sometimes see people move the APU start switch very quickly, by jabbing an index finger at it. The end of the switch rotates and although it has a rubber end your finger can deflect off meaning that you may not fully go to the start position. This may mean either that the start position was never achieved or that it was so fast it confused the electrics. Moral of the story is slow down and make any switch selections slowly and carefully.
The 737NG APU is a far more reliable starter than earlier generations but they have also offered some Mods which your aircraft may not have fitted. Most notably these were a new start converter unit and start power unit from 2001 and also ECU software is now at version 4.
S&L