Some auxiliary RAM cards put the bank select register anywhere in the range C070-C07F.
In general this interferes with analogue input reset since original II times. But on the IIe (and IIc) as well with IOU management (Double-HiRes), as they use $C07E/7F and $C077/78 (only IIc). $C074 was as well reserved by Applied Engineering for the Transwarp - after all, they did, AFAIK, come up with the idea to reuse paddle reset.
The only RAM card diverging from $C073, I know, is the Legends E, which uses $C071. Due this it needed to patch for Apple Works.
Other aux RAM cards, for example the Applied Engineering RAMWorks, only have the bank select register at C073.
It was AE that did set this standard and other cards followed. With Apple Works using $C073 to access RAM past 128 KiB, any divergence would add inconvenience to IIe users.
Most applications I have encountered use C073, but I have recently found an application, ProTERM 1.x, which I believe is using a different address in the C07X range.
Mind to share what you found? And sure it's about RAM?
Moreover, at least one set of programs, the AE RAMWorks tools, refuse to work with aux cards which have the bank register at any C07X address, since a genuine RAMWorks only listens to C073.
Seams reasonable. After all, why should they make their tool to work with other cards at all?
What was the first aux card to feature more than 64 kB of RAM,
The first was of course Saturn 128 for the Apple II. (SCNR:))
In case of AUX RAM cards for the IIe, it was AE's Memory Master IIe in 1984, with 128 KiB, allowing two pages of 64 KiB o be switched in. Later 256 KiB (4 pages) as well. This was 1985 followed by the RAMworks (I), starting a 256/512 KiB.
and at what address was its bank select register located?
AE it did set the standard of $C073 as bank register.
How did the bank select register address standard develop from there? And out of all the Apple IIe software, what addresses were most commonly used by applications to switch aux ram banks?
$C073 was common. There was no development beside increase in fitted RAM size (*1) and Apple implementing the use of $C073 with the IIc ROM 3 board - after the huge success AE's Z-Ram extension had.
*1- 16 Mi is a quite high bar to pass before needing more than one byte to switch. IIRC the RAMworks II maxed out at 5 MiB