I have a low water-usage toilet that was installed a couple of years ago. It has a barrel shaped flapper that travels straight up and down, and the shut-off float rides on a column with the valve inside. The problem is that this toilet is running intermittently, for 3-5 seconds, then shuts off again. Does this apparently randomly, but is doing it like every 10 minutes. I can see nothing obvious going wrong and I have cleaned the gasket on the barrel/flapper as well as the seat for that gasket, problem is still there. Anybody have any ideas?

Changing the seal/flapper is the most common cure.

put some food coloring into the tank water. see if it shows up running into the bowl.

The trap primer tube(small black refill tube) may be inserted too far into the overflow tube, which can cause a siphon effect.

Please post a picture.

Try changing the float level, and see if this timing gets reduced or increased, if it doesnt then the issue may be of Float.