What your describing is you have either a 200 OR 400A fluid master ball cock assembly
The great thing about Fluid master is it tells you your losing water from the Douglas valve either through a defective flapper (tank bulb) OR a broken/cracked over flow tube. The easiest repair is to replace the part the tank handle pulls up on when you push the handle down. This part is called either the flapper/disc or tank bulb. Look carefully at the type you have and go to a plumbing supply and get the exact same replacement.. The easiet way to find out if your losing water from a flapper/bulb disc is to put instant coffee in the tank and look in the toilet and see the color change in the bowl without flushing ( doesnt matter is you use decaf LOL) Good luck.