a coin mech needs power (usually 12v) AND ground, plus the coin output signal wire.
how do you expect it to work if you don't connect all the wires?
In Europe yes, because there are so many different types of coins used the mech needs electronics to determine the number of credits to issue given the coin that was inserted. In the USA and Japan coin mechs don't have any electronics and the coin is just registered by a simple, common ground, switch like any other button. Some coin doors do have 12V for a lamp to light up the reject button but that's really a feature of the cabinet design and is not tied into the game or I/O board electronics.
valid coins are determined based on the width diameter, weight and sometimes magnetism and this is handled mechanically... hence why it's called a coin "mech".
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Also I keep hearing people repeat that the coin counter pin needs to be tied to ground with a resistor... it needs to be tied to +5V not ground...
Even still, I don't think this will solve the issue that the OP is having. games that require the coin meter to be spoofed will flat out not boot if they're not connected. I've never seen a game refuse to register coin drops due to a lack of an attached coin meter. as I said they're expecting a simple common ground button just like everything else.
I don't know if the NAOMI is like this but some games do check the time that the coin switch is down if it's too short or too long it wont register a coin drop (perhaps assuming that it's being manually manipulated instead of a legit coin drop)
My suggestion: check to make sure you're connecting to the Player 1 coin switch and not the player 2 coin switch. Then I would check in the system menu and make sure you have the coin mech type set to "common". Also make sure your cost options are set to 1 coin 1 credit.
any of these settings being off could cause the coin to not register properly.
...or you could just set it to freeplay and not worry about coins in a supergun setup at all.