The rapid flashing of the neutral light - 5 times per second - indicates a fault in the electronic shifting system. There will be service code stored in memory that a dealer tech can access with the diagnostic software and a laptop.
Because only the one control is affected and the engine operates and shift correctly with the other station, it is likely either a wiring (signal) problem of something inside the control. See your dealer for troubleshooting the issue.
"There is never just one thing wrong with a boat";
-- Travis McGee, main character in a book series by John D. McDonald
The factory recommends that a properly trained technician service your Johnson or Evinrude outboard motor. Should you elect to perform repairs yourself, use caution, common sense, and observe safety procedures in the vicinity of flammable liquids, around moving parts, near high-temperature components, and working with electrical or ignition systems.
The information offered here is only general in nature and should not be construed as complete factory approved procedures, techniques, or specifications. Always use the proper service manual for your motor, up-to-date service literature, the correct tools, and have an understanding of how to proceed with troubleshooting and repair methods. If you are unsure or uncomfortable with a procedure, a situation, or a technique, enlist the services of a factory trained technician.