Simmons is not known to Play Music Man Basses, but who really knows for sure, right ? I think he plays BC Rich Punisher basses these days... As for the effect: I'd say more like a flanger.
That doesn't sound too effected to me...maybe a splash of reverb. I think what you're hearing as phaser is string rattle. I hear a little bit of phase or flange on the guitars, but not really on the bass.
He has been playing EBMM basses recently (in addition to his others). The most recent photos I've seen have been with the EBMM. Whether he played them back in '82 or whenever this song was recorded, maybe not.
He had almost the same sound on the track Naked city from Unmasked. I belive thats an MM. But im not shure if he played it himself. Maybe Will Lee did? Imo Simmons should have played MM basses more. These two tracks are the only ones that are played with MM (imo) and i think its the best bass sound he has ever had.