Frodo's necklace isn't invisible; therefore, we can assume that it does not work unless worn on a body part specifically, as he is wearing it while it is on the necklace but he is not invisible.
The real question is what body parts would work. Fingers obviously do, but would toes? Cockring? Nose piercing? Could you say that the ring being in his butt counts as wearing it? If someone can go outside wearing nothing but a buttplug, then there is some president.
Can only buttplugs be worn, or can anything be worn in the butt? Is a ring a buttplug? Cash or credit?
If someone can go outside wearing nothing but a buttplug, then there is some president.
President is the person who runs the organization or country. Precedent is the thing where an action is preceded by a similar recognized action.
But I really like the idea that someone goes out on a brisk day with their asshole whistling in the breeze because it's held open with a ring. Then, out of nowhere, the leader of the country gets mixed up in the whole mess.
I'm probably bad at explaining it, but the ring doesn't make everyone invisible, just hobbits. The ring wants to be worn so that it can exert the most control over the wearer in an attempt to return to sauron, it tempts people to wear it by giving them a taste of what they desire the most and hobbits simply want to be left alone and not seen or bothered, which is why they just turn invisible. This is also why hobbits are the idea race to carry and protect the ring as they dont crave power so it is harder for the ring to corrupt them.