That seems to vary from game to game, but at the very least the wires that need to be connected to the button should be bundled together inside the cabinet under the left flipper button. I believe some games just have the wires with no ends, while others have quick connects already attached to the wires.
Are you sure you aren't thinking of Competition Mode? I just turned on the tourney mode on my X-Men and hitting both flipper buttons at the same time didn't do anything. If you push and hold them both it didn't do anything. BUT if the left one was pressed and held...Competition Mode is available if the start button is pressed within a certain amount of time. If you try to press and hold both buttons at the same time and hit the left one slightly before the right one....this will also start the competition mode count down.
Competition mode and Tourney mode games are similar, but not the same. Competition mode should make the random awards the same for each player (just as a tourney game does). I believe extra balls are still awarded in Competition mode where they are not in tourney mode.
What tourney mode does that comp mode does not is allows you to set up the start and end time of the tourney. You can also set how much money goes into the prize pot for each tourney play as well as how many winners the tourney has and what type of tourney you want to have.
I haven't setup a tourney at my place for awhile, but when I did have semi regular visitors to my game room, I would set up a tourney to run each month. Whoever played a tourney game, paid me $1 a play and the game automatically added that $1 to the prize pool. At the end of the month the game listed the 3 winners and how much each of them had won. I also have some local friends that run 1 day tourneys when they have a pin party. It pretty handy and fun in these types of situations. The only thing I really with they would have done is made it so you could set a regular or comp mode game to free play, but make players have to actually coin drop in the machine to play the tourney games. This would have had the game collecting the tourney money automatically and also prevented people from hitting the tourney button by accident....or without paying.
Maybe things have changed since X-Men and maybe you can start a tourney game without the button now. My Spider-Man is running sys ver 1.58 while my X-Men is at sys ver 1.64. So I guess it's possible that Met has a newer sys ver that implemented starting a tourney game without the button installed.