TJ,If the ballcock is the type that has a float on the end of the rod,check the float to make sure it isn’t full of water,if it is replace it .Also the float could be out of adjustment.If it doesn’t have a float on it,most will come apart buy turning the ballcock a quarter of a turn counter clockwise.To do this you have to turn off the supply to the fixture.This type has a rubber disc in it and the disc could be bad or full of crud,clean off the disc or replace it.The ballcock will come apart about a couple of inches up from the bottom of the tank.Good luck
The water in the tank should not reach the level of the overflow pipe (what you call the “mast”). That’s your problem. Whatever kind of float-valve you have in your toilet should shut off the water flow into the tank when the tank water level is within about 1″-1/2″ of the top of the overflow pipe. Either the float needs to be adjusted or the float actuated cut-off valve is leaky. Try simple adjustments, and if that doesn’t work, replace the float valve as a unit. I like the Flo-Master units…they’re cheap, easy to install, and work great.