Personally, I think that the connotation of the word ‘elusive’ depends on how you use it. You can use it to express someone’s nature, meaning someone is hard to reach/contact/evasive, and for me that’s bad. But when used in another context, for example if you don’t want to hurt someone else’s feeling, you can give them ‘an elusive answer’, meaning ambiguous/undefinable/indistinct, so it’s neutral and not offensive. So, it depends on how you use it. I hope this helps 😄

As a word, it doesn’t have a good or bad connotation, it's neutral. It wouldn't be used to describe a person's nature or character. It's normally used with respect to the accessibility of physical things, or ideas, whether they can be obtained or understood. It could be applied to a person, meaning that they are difficult to find, track down, or get hold of for work purposes.

Interesting question. I suppose 'elusive' does have a negative connotation. However, I don't think it would be considered rude under most circumstances if it is factual. What is the sentence you want to use it in?

Elusive may be positive or negative depending on the context. Let's say you wanted to say your friend is elusive meaning very difficult to get him. This is neither positive nor negative. His answers are always elusive. Then this may be negative for people who want to know the real answers.