The graphite lock fluid comes as a liquid in a little can like the smallest '3-in-1' oil. Just shake the can then squeeze it to dribble some out. I left the tach face down overnight and may have treated it again the next day, don't remember. None of the lock fluid migrated to be visible on the face of the tach, something I had worried about but would have considered acceptable on that YM186D.
My YM240 (YM2000 equivalent) was like you described yours, it showed years of 'neglected maintenance' but fundamentally sound. After a month of tinkering repairing/replacing minor stuff like those dash lights it has been flawlessly reliable since, 13 years now. It still looks thrashed, I've never done anything about its appearance.
Discussion here indicates it is impossible to have the warning light's sensor and a gauge's sensor both immersed in hot water in the 'thermostat housing' (there's no thermostat) - you have to mount one or the other. I've read of people splicing metal into the upper radiator hose to make a mounting point for a second temperature sensor like was done on some old tractors that never had a sensor. I wouldn't do that. My own preference is just get the OEM sensor/light system working and don't worry about it.
That the clutch won't fully disengage might be the linkage is too long or short. Look to see if someone hacked in some linkage component that isn't original. Between 3 Yanmars purchased at over 25~30 years old, I've found and replaced cobbled-together brake linkage rods on two of them. I suspect the originals broke when adjustment was attempted but the adjuster threads were rusted. if you find some hand made parts in there replace them with Hoye OEM replicas. I'm a strong believer in restoring everything to as close to original as possible, it makes everything easier to understand.