Purpose of HC-05 red button - FYI

If your HC-05 board has a red button, I've found that it has two purposes:
1.) Press it while powering the board on will put the module into "AT" mode;
2.) Press it while the board is in normal mode and you can enter "AT" commands, e.g. in a script.

Note that what I also found with my board is that even though I'm in "AT" mode, certain commands won't get a response (AT+NAME?, e.g.) but if I press the red button the command gives the correct response. So, if you're in "AT" mode and you don't get a response to a command, try pushing the red button. I don't know if it's connected to a pin or not; but on my board I only have 6 pins( vcc, gnd, tx, rx, en, state) so it wouldn't matter to me if there was a pin associated with it or not. Maybe if someone has a breakout board you might have access to the pin associated with the red button and could programmatically ("press") it.

Just a FYI tidbit

I understand the button simply bridges between a point downstream of the power regulator and the EN pin. This means that it does not matter which is used, and thus you can still go into configuration mode under software control, you just need to control the power supply as well. It also implies there are no exclusive commands or controls associated with the button.