Rather than focusing on how you will discipline your son, I would suggest that you sit down with him and allow him to explain what a nearly empty bottle of rum was doing in his drawer. Listen to him without interrupting first. My guess is that you will get a defensive responsive that will not be entirely truthful. You need to convey to him that you are concerned if he is drinking secretly and that in your family you don't keep secrets like this from each other. He obviously knows that the law forbids him to drink alcohol. The key concerns are why he has been drinking, how long this has been going on, how much, and how often he has been drinking, and what you and he are going to do to help him stop drinking.
Experimenting with alcohol at age 16 is, unfortunately, not unusual. Rather than shaming or condemning him for drinking, I would emphasize how much you love and respect him and how you are going to do whatever it takes to help him end this behavior. You certainly can ask open-ended questions like, "Are many kids your age drinking too? Do you think it's okay for you to drink? Would you be worried if you were in our place and discovered your teenager was drinking? What do you need from us to help you to stop drinking?"
These questions show your concern and your attempts to understand why he has drunk, rather than asking him questions designed to make him feel guilt and shame.
This discovery and your discussions with him can strengthen your connection with him. It may be the beginning of his experimentation with alcohol, or he may have a drinking problem. You need to find that out. And you must make this the first of several discussions that you have with your son about drinking and drugs.
If you have never had these discussions before, it makes it more difficult for your son to come to you with problems he is having in these areas. So open up the door to healthy, give-and-take discussions -- not lectures -- about drinking, drugs, smoking, and sex. Let him know where you stand and why on these topics, always being mindful to share your values regarding these behaviors. I believe that good things will come from this discovery as long as you underscore all your discussions with love, genuine concern, empathy, and support.