I have a 1988 200hp Mercury that is having 2 problems but I don't know if they are related.
Problem #1: It has problems idling. Idles rough and sometimes willl backfire (sneeze) and die.
Problem #2: Acts doggy whenever run out on top-end. The engine will max out a 4800 rpm. After running for a few minutes (varies each time) it will all of a sudden kick-in and run like a race horse and goes on up to 5600 rpm.

What I've done:
Tore down the carb and cleaned it but I didn't put in any new parts, it's possible that some of the needles are sticking.
Coils are all sparking but I haven't measured the exact voltage.
I have measured the resistance on the stator (ohms) and the R-gnd reading is 85 and RW-gnd is 84. According to my repair book the reading should be 125-175. The output voltages are are 110V/AC on the blue and blue/white wires and 38V/AC on the red and red/white. Are the resistance readings or voltages too far out of spec?

I haven't gotten into checking the timing or the response of the timing advance "black boxes".

Any ideas? I don't want to get into the shotgun approach of changing parts until I find the problem.

PLEASE HELP!!!!!

Coughing and sneezing at idle usually indicates dirty carbs.
Use Mercury Power Tune or Valvetect carbon remover to soak carbs for a few hours and then blow them out.
If your carbs were pretty dirty you won't get them clean with normal carb cleaner.
Needles are cheap. So are floats
You will not get an accurate test of voltage output with any meter other than with a peak reading meter or a DVA adapter attatched to your DIGITAL meter.
Rarely if ever does the timing change on a motor such as this. Usually once it is set correctly it will stay for the life of the motor. If this motor has been around since 1988 chances are the timing is OK.
To check the Bias circuit on the switch boxes disconnect the white/black wire from each box and check continuity to ground from the post on the switch box. It should be 1200-1400 ohms.If it is out change BOTH boxes.

Thanks for the feedback, I will proceed to see what I can find out.

also a sneezing can be lack of spark

the problem ended up being the low speed/high speed "black box".
I found out that they are no longer available and are not needed.
All you have to do is disconnect it and do a "link & sync".

I did all of this and now my boat runs better than it ever has in the 14 years that I've owned it!

yes the idle stabilizer