I found out why this occurs and how to resolve it. According to the docs:
Note: The returned email is the user’s publicly visible email address
(ornullif the user has not specified a public email address in their
profile).
In your GitHub profile settings, under Public email, some users (including myself) have that option set to “Don’t show my email address.” The call to /user only returns the public email address, so if the user doesn’t want it shown, the API will respect that.

To get the user’s email addresses regardless of whether or not they are public, use the call to /user/emails. You would use the access token in exactly the same way as the /user request:
Accept-Language: en-us
Accept: application/json
Authorization: token 83f42..xxx
Accept-Encoding: gzip, deflate
GET https://api.github.com/user/emails
This call gave me the following JSON response:
[
{
"email": "user@example.com",
"primary": true,
"verified": true
}
]