Ikari Warriors on a multi-JAMMA board? Well I would have no idea about that, but real Ikari Warriors boards have a pair of connectors on them which you connect the rotary switches on the joysticks to, via a 13-wire harness that comes with the joysticks. The rest of the joystick (the 4 microswitches on each joystick that provide the 8-way directional control) connect to the board via the main wiring harness, the same as any other joystick.
Ikari Warriors uses 12-position mechanical rotary joysticks (a distinct mechanical click for each position). You can use SNK LS-30's like came on dedicated Ikari Warriors machines, and there were also Wico and Data East versions that will work. Happ Controls makes a 12-position mechanical rotary joystick that will work as well.
You are not going to be able to hook up the rotary switch part of rotary joysticks to a multi-JAMMA board unless the manufacturer of the board has specifically provided the provisions for you to do so, which would be in the form of a pair of 13-pin headers on the multi-JAMMA board. So I guess you should look for something like that on your board.
Have you tried the game out yet? It's possible that they used the version of Ikari Warriors that lets you play the game with ordinary 8-way joysticks. This is a hack which aims your playable character's gun in whichever direction you push the joystick—in the manner of Capcom's Commando (1985).