I have an 89 LX 2.3L 5 speed manual hatchback. I have noticed that the turn signals have recently gotten pretty bad to where they will not flash at all if you push the stick all the way down or up to make a left or right turn. They will flash in certain spots when you turn the wheel - typically around 10:00 to 11:00 for left turns and 1:00 to 2:00 for right turns. If the wheel is dead center, or past these positions, it will not flash. Tonight, when I got home and was backing up into my spot, I noticed that the reverse lights would turn on and off, and I wondered if it did it at the same time as my turn signals. I tested this and sure enough, my backup lights would work at the same time my turn signals would work and quit when the turn signals quit working.
It could be a variety of things. Turn signal switch/multifunction switch, ignition switch, a wiring problem in the column. The first thing I would be looking for is a broken or loose wire since your problem is occurring with steering wheel input. You will need to remove the plastics and expose the steering column, then turn on the turn signals. Try to tug/wiggle the wires and see if you can get the signals to quit working. If you do, then you will need to track down a broken or loose wire. JRichter has been a good source on these forums and probably has posted or can provide a wiring diagram that would help you out.
The ignition switches in these cars are really problematic and can cause some weird and seemingly unrelated electrical issues. Since you are mentioning reverse lights, it is something to consider. I do not know what, if any, wiring is shared between the turn signals and reverse lights.