04-09-2020 08:24 - edited 04-09-2020 08:26
A charged up battery should read about 12.6 volts. Your one battery size is the absolute minimum for your engine and the other is too small.
From your description it sounds like the solenoid may be faulty, but it should be tested per the factory service manual or by a trained tech. A voltage drop test would be very enlightening.
The minimum battery specs for your motor do not take in account the electrical requirements of your boat's systems.
From the owners manual:
Battery, Minimum 675 CCA (845 MCA) 12 volt or
800 CCA (1000 MCA) 12 volt below 32°F (0°C)
"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.