Thanks to @Dmitry's comment above, I was able to resolve this issue by configuring the default plugins for Tern.

In the `tern` file from the repo under `bin/tern`, I edited the default plugins here:

    var defaultConfig = {
      libs: [],
      loadEagerly: false,
      plugins: {"commonjs":{}, "node":{}, "requirejs":{}, "node_resolve":{}},
      ecmaScript: true,
      ecmaVersion: 6,
      dependencyBudget: tern.defaultOptions.dependencyBudget
    };

Where I changed the `plugins` property from `plugins: {},` to `plugins: {"commonjs":{}, "node":{}, "requirejs":{}, "node_resolve":{}},`.

Now `tern-find-definition` is working well! 

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Furthermore, for the false-positive `require` statement error, I was able to correct this by running `M-x customize group RET js2-mode` and enabling `Js2 Include Node Externs`.