Oil runs droplets from small hose

Hello dear people, thank you so much for getting rid of my questions here I recently bought a scooter: Peugeut Looxor 50. At first it was very difficult to get the scooter. The E-starter didn’t manage it and I had to kick very, very often until I got it. He also went out more often after some time. After many attempts I managed to get started and drove about 20 minutes over the field paths. Suddenly there was a very bad way. önes noise and the engine suddenly went out. I could turn it on again, but that happened immediately after 50 meters again. Now the starter was blocked and let itself be moved nciht more. Then I pushed it home and disassembled it with a friend, cleaned the carburetor, refilled some oil. We managed to get the engine to run again – because of fear of breaking it we didn’t drive with it anymore. Now to the own I have a problem (I think): We have assumed that the engine does not get any oil and therefore has become much too hot. During the dismantling we noticed that the “footroom”, i.e. under the feet, is full of oil. It came out afterwards that there is a small hose that does not lead anywhere and loses drop-by-drop oil when the engine is running. However, I don’t think this is directly starting from the oil pump, as it sits further down. Here’s a picture: Can someone help me? E there is also somehow nothing nearby where the hose could have been on it. The black hose looks very closed and it would be funny to just put the hose on it.