The infamous "mercury sneeze."
Either too lean or too much throttle plate opening combined with retarded timing, or a combination of all 3. Or carb sync is off a little bit. Or the pilot jet is partially clogged in one or both carbs. Also double check-some of them had 2 different main jets, one was slightly larger than the other and can aggravate a sneeze. I don't remember what timeframe they were doing the split main jet sizes...might have been 06-later.
Air leaks are not very common on these. Most everything uses O-rings instead of gaskets, but it is possible that a carb mounting O-ring can be missing.
Another thing to consider is the cowling. Once the engine is running close to right, you can adjust the idle mixtures slightly lean. Once the cowling is back on, it will richen up just a shade due to air flow restriction of the cowling air intake. The carbs on these motors are a bit sensitive, but it is nonetheless a great little motor!!
Timing at idle should be 7° ATDC +/- 2°. Pickup timing should be 0°. Max timing should be 25° BTDC +/- 2°. If you are real careful with fuel quality and ONLY run 93 octane, you can get away with up to about 28°. Helps a little bit. Check the timing-it has a big effect. No telling if anyone's monkey'd with it in the past.
Also on the carb sync, it's easy and doesn't require any special tools. Loosen the idle speed screw on the bottom carb until it no longer contacts the arm. Then in the middle of the throttle link is a screw. Loosen the screw and look down inside the throat of each carb. They should both be totally closed. If they are, tighten the screw. If not, you can move each throttle individually a little until they're both shut completely. This also makes a big difference in idle and low speed running quality.
Mixture screws, if they haven't been tampered with, should be your last adjustment. It's easy to start cranking on 'em but if they're close to 1 3/4 turns out already, leave them until everything else is done. I like to get the idle speed about 850 RPM in neutral, then start fine tuning. You can retard the timing at idle but once you get to about 7°, it will start to sneeze a little. I've done a couple in the past that I could not get them to 7° and maintain a good idle, so a lot of times I had to advance it slightly to regain control of the idle quality.
If done properly, it should idle in neutral cleanly at 750-800 RPM, and in gear at about 650-700 RPM.