There are several ways you can authorize someone to make changes and request information about your account.
Email ticket
The safest method is to change your Ticket System password, and then give the third-party that password. They will then be able to visit https://tickets.hostgator.com/ and login with your primary email address and that password. An additional benefit is that you will get an emailed copy of each conversation between the third party and HostGator.
WARNING: Be sure to change your ticket system password so it is not the same as your billing account password. Also, it is NOT recommended to give any one your primary email's password.
Live Chat
You could simply provide the 3rd party with your verification information, such as the last 4 digits of your credit card or your security PIN. However, this is very risky, and not a good idea.
Phone call
You may call us on the phone, verify your identity, and then put the third party on the phone to ask the technical questions.