I've had similar problems with an IPAC (an older version) when the ground loop gets overwhelmed by something else, for example an arcade DC power supply for the audio amp.
For me, the two problem buttons were furthest from the IPAC (["shift"/enter/admin] and [pause]), partially hidden up under the marquee, so longest signal loops and possible EMF interference (from the CRT or speakers themselves). The buttons kept registering ghost presses.
Using a line filter on the AC into the DC power supply helped, and using an audio ground loop isolator also helped.
Check the flashing self-test LED on the IPAC as you turn on PC. The number of flashes is a code which can tell you which buttons are shorted (I don't know where to find the table to interpret this for your IPAC Ultimate though, ask Andy). In my case the IPAC seemed normal on startup (2 quick flashes then stays on), despite the issues.
https://www.arcadeworlduk.com/pages/IPAC-2-Code-Table.htmlTry disconnecting wires from the 2Coin completely. See if problem persists even then (it might move to another button!).
Try disconnecting anything that might be causing group loop interference.
Try a ground isolator. They are relatively cheap and come in various forms. get one with 3.5mm jacks you can plug it right in. Example linked below.
https://www.amazon.com/BESIGN-Ground-Isolator-Stereo-System/dp/B06XQYN77L