My first guess would be driven water getting into an electrical connection (around the spark plug wire itself maybe). Second guess would be water somehow getting into the combustion chamber (through the airfilter mod maybe).

try cleaning the stop/run switch.

it's likely to get wet in the rain or hot in the sun.

yeah, on the grip.

people have said it gets dirty and causes problems.

This concern came up many years ago on Bert's German Savage forum. I believe it is caused by the carb icing up. When the humidity is high and air pressure is dropped (going over an airplane wing or in the carb venturi) the temperature drops and moisture in the air sticks to and freezes on the surface. Air temps can be up to the 50's as understand it from my flying colleagues. Wing icing has been the cause of many plane crashes, that is why the de-ice airplanes before take off when it is snowing, freezing rain or other conditions that promote icing. The temp drop is caused by the venturi effect, not the ambient temperature. What you can do is the next time  it happens, look down at the carb and see if there is frost on the outside, if so you have your answer as there is frost on the inside which changes the carb air bleed holes, may stick the throttle in one position, and lowers fuel mileage as the air bleeds are plugged. If there isn't any frost, quickly touch the slide area of the carb and see if it is ice cold as there can still be frost on the inside. Mine has never done it or I would have a answer for you. I've had 2 vehicles that did it. 54 Mercury with what was called a teapot carb, It would frost up inside and out, to the point the throttle linkage would not move. As it frosted off most of the air bleeds mileage went in the toilet.  2nd one was an 81 Chrysler K car and even with heated air from the exhaust going into the air box, it would "ice" at 32 -34 degrees when a heavy wet snow would be falling.  Only did it 3 or 4 times when conditions were just right. Park and shut them off for 10- 15 minutes and they would melt and work OK for a while or until the relative humidity/temperature relationship changed enough to prevent it. Please do let us know as it has been an unaswered question since 1998 that I know of. Max

How cold is the rain? I would figure if the rain is really cold and it hits you after you have been riding a while. The cold rain is cooling off your engine too fast making it sputter the way you are describing. Unfortunately if that is the case, there is nothing that can be done about it. Using a water hose to try to duplicate the problem then wouldn't work because the water out of the tap would not be as cold as the rain.

Here we go with the spray bottel of water. start your ride let it get hot. start spraying water up under the fuel tank do both sides  {don't use a hose} If she starts to miss or run rough Take a real good look at  the coil and plug wire  There is no wire boot at the coil water will get in and it will short the plug wire. Water will also cause the spark to jump to ground at the plug if that boot isn't sealed eather  When checking the coil plug look for what mite look as a pencile line on the surfaces this is carbon tracking this is were the spark has found a path out to ground.  The coil and plug wire are very negleted parts  Just a thought
Ride on
Viper

Thanks all for the ideas.  I think that I have found the culprit.  I have tried this before but an old harley wrench head friend of mine got challenged by the mystery this weekend.  He took the hose and cut it down to a very small but rather powerful flow of water and then with me holding the throttle open a bit he went over the bike.  When he hit either of two places it would start stumbling.  Either of the two large diameter hoses for the carb.  I am speaking of the one that goes from the airbox to the carb and the one that goes from the carb to the engine.  We would let it work its way through the water that had gotten in and see if we could make it happen again.  After a number of beers and attempts we were able to make it stumble basically on cue just by playing the water hose onto either of these air/fuel hoses.  I have since tightened up the hose hands that secure these hoses.  We will see what happens next time it rains while I am in transit.  If that dose not fix it I am going to assume there are pin-holes in these hoses and replace them.  I had set my idle speed a 1/4 turn too fast bcause in the mornings as many have also discussed I was having low idle problems for the first 10 miles or so.  This problem "seems" to be gone as well.  This could be the cause of both problems.  Will update when I figure it out.