I recently had similar problems with mine and i got it fixed with some adjustments , new eccentric as well as shift shaft. If there is any wear at all on the shift shaft replace it , same with the eccentric.
With a good shift shaft and eccentric have someone on the left side of the bike shift the bike into the gears and the shift drum should put the spring loaded roller right into the lower valleys on the shift star. If it doesn't "clunk" right into gear and the shift shaft/claw doesn't rotate the drum all the way and put the roller right into the lowest part of the shift star then it will give you problems and false neutrals and potentially break something. Also make sure your eccentric is almost bottomed out and do your adjustments in 2nd gear putting the claw with equal amounts of space above and below the 2 pins. I also like to use loctite on the eccentric if you have it and get the 17mm nut on it pretty tight and use the locking/ bendable washer to hold
it tight.