Hi, apologies for the noob question

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I would like to buy a coin door for my scratch build arcade cabinet and the info states that you need 12v and ground either from your jamma board or your PC motherboard.
I was wondering if I could supply 12v to illuminate the button's via a 12v adapter (see attached). I would be using the screw connector terminal as circled in the picture.
Would I be correct in assuming the positive from the adapter would go to the 12v connection on the coin door and the negative from the adapter would go to ground on the coin door?
Would this work?
Thank you in advance.