I have a couple of possible sources for your toilet water drip but I would have thought your plumber would have been specifically looking for my proposed sources....it's just so common I think he would have been looking for it. I assume the drip IS from the toilet since it stops when you turn off the toilet source water.

The answer might be different, or troubleshot differently, depending on the type of ballcock your toilet has....the system it uses to fill and shut off when the tank is full. If I had to guess, I would say the valve that shuts off the water when the tank is full has a small leak. When the tank fills, typically, a float rises with the water level and eventually rises high enough to shut off the fill water. If that valve leaks a bit, the drip will ultimately raise the water level enough to enter the overflow pipe and enter the toilet bowl.....one drip at a time so you won't notice water entering the toilet bowl at that rate. The easiest way I know to check for this issue is to leave the cover off the tank on the back of the toilet and either watch for the drip....or look to see if the water level rises to the overflow line after some period. If the drip is very slow, water might even be evaporating from the tank faster than the drip is filling it.

One other possibility is very much related. There is in many/most ballcocks a small flexible line that ends just inside the overflow pipe. This line helps to refill the toilet bowl as the tank is refilling. If the drip is coming from this line, the drip will be bypassing the tank and dripping down into the toilet bowl (via an inner route). You can pull this flexible line out of the overflow pipe and watch it for drips. If it drips, the solution is still replacing the ballcock.

John, I've had those issues you described in the past, so I jumped to those right away. I have an extensive background in R/R toilet innards, none of what you just mentioned is an issue. Why you ask, that would require the toilet tank to drain. If you read my issue thoroughly, you will note that the tank DOES NOT refill at periodic intervals throughout the day or night at all. Additionally, I would also see water agitated in the toilet bowl if it were coming out of the overflow line and the overflow itself, as those noises are would make a rookie take notice. I've inspected all the pieces with a fine tooth comb. The system doesn't have a "ball cock" assembly, but a more modern tank filling assembly. I don't want to waste the $$ on buying a bunch of equipment an the problem is not rectified.

If you don't find it after doing as John9A said here's something else easy. The flapper (rubber piece pulled up by chain each time flushed) can become brittle or otherwise not seal 100% when it returns to seat. Wipe both contact surfaces with rag or paper towel then apply a thin layer of Vaseline to contact surfaces. If drip stops ,replace flapper.

HI, Does the water ever stop dripping? On newer homes like less than 20 or 30 years The drain lines are ABS or PVC. Those type make more noise that Cast Iron. When you flush the toilet a lot of water leaves the toilet, but some water will hang around on the wax ring and drip off, with cast iron you won't hear it with the other types you might.

Good Luck Woodbutcher