I don't think I've used any Accushift Plus+ components. But my '89 Ironman came with the Suntour GPX group. It is picky, as Suntour's own tech manual advises. But not impossible to set up satisfactorily.
I got the best shifting with a
SunRace 7-speed 13-25 chromed MFR30 freewheel, combined with a KMC Z72 chain. Snick-snick from the downtube shifter, no clunking sounds from the rear derailleur, no slight rattly sound from the chain.
Once the right components were in place, index shifting with the GPX group was a delight. No need to finesse anything, such as slightly over-shifting in certain cogs to be sure it connected.
I also replaced the original plain Suntour 52/42 chainrings with Vuelta. The 39T small ring is plain, but the 50T big ring is ramped and pinned, and shifts much more smoothly than the original Suntour 52T. No more dropped chains or hesitant shifts on climbs.
In comparison, the original Suntour Alpha 7-speed 13-24 and my recent replacement 13-26 freewheels are picky. They lack the fancypants tooth shapes of the SunRace, which was borrowed/stolen from Shimano's designed. The Suntour freewheels do not like the fancy KMC chains like the Z72 and Z50, with shaped, beveled/chamfered side plates. Those chains invariably cause slight rattling in the middle cogs as the Suntour freewheel wants to grab the chain and shift no matter how much I fiddle with drivetrain adjustments. The Suntour prefers plain sideplate narrow chains, so for now I'm using a KMC Z33.
I'm gonna try @
dddd's suggestion to try a Shimano 9-speed chain. But for now the Suntour 13-26 is behaving acceptably with a KMC Z33 that I already had -- it was slightly used with another bike/freewheel, so it's probably not an ideal example of what to expect from a plain KMC narrow chain.
No idea if any of this applies to the Accushift Plus components.