If self switch A triggering was going to cause switch 2 to NOT trigger, then the dialogue between the two commands would also not happen.
Please show us what is on the second page, and what makes you think switch 2 is not being turned on? Have you actually verified this, by debug (F9)? Or is it just that something else you're expecting to happen due to switch 2 being on is not happening, and you're assuming the problem is that the switch isn't being turned on?
Is there anything that could be turning the switch off again straight away? A common event set to parallel process, another event on that map set to parallel process, a script that uses switch 2 for something as a default, that you haven't configured to use a different switch?
Yes, it is probably an issue with a script that is turning off your switch because you haven't configured it. This is the third time I've said this and asked you what scripts you're using. You have yet to answer.
Using a different switch and getting a good result might solve THIS problem, but it's not going to stop others from happening down the track. You need to understand WHY it isn't working, so you can make sure you don't continue to make the same mistake.