What is the connection between enlightenment and non-duality?
Well, enlightenment IS non-duality, but enlightenment is also beyond non-duality. Duality, non-duality, enlightenment are just words, concepts which people use to describe what happened to them and how their experience of life changed. So, they are fundamentally relative, they are not true in the absolute sense. Non-duality is also just an idea.
That doesn’t mean that the experience of non-duality isn’t real. When/if non-duality happens to you as an ongoing experience, you will understand what other people mean by it, but unfortunately, not before. Ultimately you are always in non-duality, which is also duality, but the mind stops thinking about this philosophical stuff after a while, which is kinda the point. A cup of tea will always be a cup of tea.
One might say that non-duality is a stage in the spiritual journey (from self-realization to complete enlightenment), after which there is no more difference between duality and non-duality, and the very concept of enlightenment loses its meaning. It’s a necessary stage, during which ego undergoes its complete dissolution, and it usually lasts several years (sometimes 10 years or more).