Your edit is correct, they did have one model of the 1200 with FI, but not the 1500. Didn't come into play until the 1800.
FI was on 2 years of 1 model bike. 1985 SE Wing (Brown) and the 1986 SEi Wing (Cream), both 1200's.
Had a 86, and now I wish I'd of kept it after I got the vapor lock cured. They located the fuel pump toooooo close to the exhaust. When ya worked the hell out of the bike in the heat, like down South, she would vapor lock real quick. Once I figured out what the problem was, we stopped and bought my daughter a 1,000 squirt water gun. She was instructed to fire at the pump when I hollered at her in the intercom. She got us from Tallahassee to Chillicothe, MO in one day, keeping the pump cool. Last 500 miles of the trip was in the rain so it kept itself cool.