1990 Pontiac 6000 - rough idle and backend whine

171k miles, bought recently, ran fine for a month. Now it has a very rough idle, and it runs rough when I am at a constant speed - but not when I accelerate or decelerate. Mechanic says no codes but when he watched the numbers it indicates multiple misfires and recommended a tune-up. Wires and plugs are fairly new, but he recommended changing them anyway (for $150!)
But when I shut the engine off there is a very high pitched whine coming from under the back near the fuel pump. It whines for a few minutes then stops. Don't know if that's related.
Any help appreciated!