You have the older type of separate cistern & pan, connected by a flush pipe.
The leak is either where the big plastic backnut tightens up under the cistern (rubber washer inside), or where the syphon is fixed to the cistern itself.
Syphons are quite crude, simple devices. Even after a flush, there will always be a dribble of water left that runs on. If it's a lot, then just replace the syphon. They're not at all expensive.
The other thing is that your older type syphon has been replaced with a modern type that incorporates the overflow. In that case, the float level may be too high, and water is constantly overflowing into the bowl.