It now seems the question here is not about the final drive, as in the belt between the output of the engine and the rear wheel sprocket, but rather what Kymco is calling the final drive in the service manual. I opened my pdf of the SM and looked into this a little deeper. The reduction gear set is likely what the OP is asking about. Based on what I am reading and seeing in the SM the clutch is located in the "mission box" or "mission case" in both the chapters that cover the wet clutch and the final drive (reduction gear set). That final drive is a set of 3 gears that reduce the output of the clutch for the input to the belt drive sprocket shaft, or what is officially called the final shaft. I think this is the gear oil box that @cerberus refers to and is asking about. This reduction gear set sits in a gear case behind the mission box and is open to the wet clutch. From what I can tell the oil in the wet clutch mission box, which is the same oil shared by the engine, is siphoned from the rear oil screen under the clutch up to the reduction gear set gear case to lubricate those final drive gears. It then drains back down into the mission box to the clutch. There is NO separate sump of oil for those gears but they share the engine oil same as the clutch does. Yet another reason there are 2 oil drains and 2 oil screens that need to be pulled to drain the engine/clutch/gear oil. It's all the same oil reserve. So when you change the engine oil you are servicing all those components at the same time with one oil reserve. That's a really well thought out system if you ask me... as far as performing service is concerned.
So to perhaps answer the original question: there is no separate oil drain location for the final drive gear set but it is the same oil used by the engine and clutch and the 2 engine/clutch oil drain plugs are all that is needed to service the oil for that reduction gear set. It's all one oil supply.
BTW - the service manual I have is for the Euro 4 AK 550 and is a free pdf download from the Kymco.at. Go to that web site, then Downloads, then Technical Downloads. Scroll down the list of many Kymco scooters they have manuals for and the AK 550 is down most of the way in the list. The complete service manual is called Workshop Manual. There are also the electrical diagrams and Service AK 550 manuals (the service manual is a subset of the complete SM). These manuals for the AK are in English. Don't know about the others. It's a FREE download so no reason not to have it on hand to provide the kind of information asked about in this thread!