Re: Honda 130 hp rough idle
The Honda 130hp motor is an injected motor, hence no carburetors, so no worries about idle speed jets.
Is there spark at the connector for the #3 plug at idle? Make a good connection with a wire to the terminal in the connector, then hold the other end of the wire 1/16" from the block while the engine is running at idle (be careful not to get any spark near gas fumes!). If you see a hot white spark then perhaps your #3 cylinder is getting flooded such that the spark cannot ignite the mixture in the cylinder. If you get no spark, or a weak yellow spark, then perhaps your coil or sparkplug wire is bad.
Try swapping parts with other cylinders to see if the problem follows the part from the #3. If it does, then the part from #3 is likely bad. For example, swap the injector from #3 with one from another cylinder. If the #3 then fires properly but the other is then wet, then it's likely the #3 injector is bad. Or, if swapping the sparkplug wire and coil with another results in no spark/weak spark on the other, but strong spark on #3, then the original #3 wire/coil may be bad. If #3 remains the bad one no matter the foregoing swaps then perhaps the issue lies further upstream in the ECM or the magneto.
Good luck.