Tohatsu Problem

Hi, all!
I have an issue with Tohatsu tiller 20HP. I heard that this Tohatsu motor is the same as Mercury 20HP and moreover Tohatsu makes it for Mercury.
The problem is that every time when I lower the speed/RPM from (relatively) high to minimum or near the minimum, the motor makes a strange, not right sound, starts shaking/vibrates erratically and the red light lightens up.
First several times when it behaved like this I stopped the motor immediately. Then after some time tried to start it again using the rope but it did not allow me. It seems like it was engaged in the gear. Then when I tried to switch it from neutral to start and neutral to rear it would allow me to switch only to forward but not to rear. I had to pool/push the handle several times and once even to reach the propeller and turn it when it was engaged, and only after that I was able to start the motor.
Last time when it happened I decided not to stop the engine due to circumstances and the motor seemed to work normally after some time but the red light did not shut off for a few minutes before I finally stopped the engine.
It appears that there is something wrong with the shifting but I would like to ask for any ideas to start and what to look first for before starting to dig the motor myself. Professional marine mechanic is not an option for me.
Also does anyone know if something similar to the OBD II reader is available with these motors?
Thanks a lot! Any suggestions will be highly appreciated!

Red light for overheating or? Have you checked at https://forums.iboats.com/ they have a forum there for Tohatsu.

Red light on this motor is for ‘everything’ (overheating, overload, too high RPM etc.). Manual does not specify that.
Thanks for the forum link. I’ll check it out.
So far, I disassembled the lower unit and everything looks pretty good. Nothing wrong is in there.
It seems to me that the problem is most likely in the shifting rod, it is either a bit shorter or a bit longer. There is a possibility for small adjustment but the question is why it could go off.
I got the boat with the motor in 2018, brand new, and never abused it much.
To adjust it properly is going to be a big headache, because it worked well before most all the time except when I went from high RPM to low RPM. So the adjustment should be done in a real working situation, not in the garage.
Without any experience it may take forever.
Thanks for the forum suggestion, I’m going to check out tomorrow and may post about my situation.