The "ignition" wiring harness, meaning the actual spark plug wires, are replaced every 60k miles and cost about $35. This is a job you can do yourself, or ask your mechanic to do in about ten minutes.

The "engine" wiring harness consists of a large collection of bundled wires leading to and from various sensors and controls. In pre-88 cars, it deteriorates because of faulty wire insulation. You buy it as a unit from a place such as IPD and install it as a unit. It is time-consuming to replace.

It has nothing to do with the alternator function (unless the wires are shorting). You can remove the alternator and have it completely rebuilt at an auto electric shop for about $75.

TIPPI:
Who is the fortune teller you are consulting? ALL 240 and 740 from 1982 to 1987 had the deterioation of the wiring harness as a matter of course. A new one from Volvo is MEGAbucks ($400)...a good used one from Dave's Volvo Harnesses is reasonable ($160)
YOU should become educated and replace it yourself...takes about 1 full day.
The alternator is another EASY job. Rebuilt aftermarket ones are about $100 and replacing one is "Pappitas" = no sweat.
Give it a try and you will go far in Brick repair. No one will take as much care as you will.
buena suerte,
el Raidman