Please describe what the rule should do:

Disallows duplicate test conditions in if-else-if chains.

What category of rule is this? (place an "X" next to just one item)

[X] Warns about a potential error (problem)

Provide 2-3 code examples that this rule will warn about:

if (a > 1) {
    foo();
} else if (a > 1) {
    bar();
}

if (a === 1) {
    foo();
} else if (a === 2) {
    bar();
} else if (a === 3) { 
    baz();
} else if (a === 2) {
    quux();
} else if (a === 5) {
    quuux();
}

Why should this rule be included in ESLint (instead of a plugin)?

It's a possible error. A statement with a duplicate condition can never execute (unless it's an unusual use case with side effects).

This rule is similar to the existing no-duplicate-case. The error could be due to a copy & paste and a long chain.

The test nodes would be compared by their tokens.

Are you willing to submit a pull request to implement this rule?

Yes.