A focus light is a seperate light to give you enough light so AF can work well. While it may help eventually , I would suggest Auto focus may not be a huge amount of help to you until you master the correct technique.
The problem you have is that the working range is very limited. If you try to rely on AF and you are not inside this very limited range AF won't help you at all as it won't find anything to focus on. So you need a proper routine to get the camera in the right range. You have to be very stable in the water to stay in this range. If you fall outside the range nothing will be in focus.
MF is probably the best option - at closest focus of the lens the point in focus is 55mm from the end of the diopter and at infinity focus the point in focus is 75mm from the end of the diopter. At closest setting the area covered will be 35 x 23mm. As I described slowly move in until you can see your subject and rock back and forth till it's properly focused and take the shot.
You can try AF but you still have to slowly move the camera into the correct position watching the screen till it comes into focus - wait and do not try to AF till you can clearly see the subject. If you hit AF early it will just hunt. I'm not sure what AF is like with diopters on a RX100V but it's likely to be slow.