In Attract Mode you can set up more than one button to do things, so if you set up attract mode using one device e.g your trackball, and then once you have the other controller in, then set that up as well.
So to give an example Controls
Quit - Add Input Esc and as long as you can get in the menu system again, which you should really have a keyboard attached, then you can map the other buttons just by going back to Quit and add another input. So it will save two different inputs so if one is not plugged in, then it will see the other and work (or should do)
Firstly, you are using someone else's image so that is classified as not a stock version of Attract Mode.
Attract Mode is open source, so you might have someone do modifications to it and then place it onto an image with changes that are not present in the stock version.
Also this is not the ES (Emulation Station forum) wrong turn Clyde.
So really you need to ask in the ES forums.
You are asking us about an image that you have, that we might have never seen before, so we do not have a clue about how it works.
However, do you have a keyboard installed at the same time? Silly question, but cannot you program buttons on your control panel, and then use keyboard presses for the rest?
If you just go to Youtube and look at ETA, CoolToy then you might find some information out that you might not have known. I have seen the videos before and I remember them setting up ES and I think it was two buttons that they held down to start skipping.
The majority of your question is mainly about other software and as I said before, unless people have got Arcade 1up cabinets, then they will not have experience of setting it up.
Skip to 15:00
https://www.youtube.com/watch?v=wyRKFY9F3yY set up of ES or 15:19 where it says hold any button to skip. So if you hold down a button then it will skip that button rather than having to map it, even though you have said that is not working for you.
Regards
Mark