To login with an admin account with project zomboid you must edit the command line. The command line is the first thing the server sees before it turns on. It contains information which, in some games, are used for information that does not change like map level, rcon passwords, etc. To do so is very simple.
First, log into your GameServerKings Game Server Management Panel and login using your TCAdmin information provided to you within yoru verification email. Once you login, click "Game Services" on the left hand side of the screen, in the navbar nested under "Game & Voice Management"
Now that you're in your game services panel, click on "Commandline Manager" and once you're in you will see two tabs at the top. One titled "Predefined Commandlines" and one titled "Custom Commandlines" click "Custom Commandlines"
Within the "Custom Commandlines" tab, click "New" in the top left hand corner, and give a description to your commandline. For this example I'm using "MyServer." Then, click the checkmark next to the "Admin Password" field and within the field type in a secure password. The password I chose, was SecurePassword.
Take a look at the other options while you're here and set them up as you like. When you've finished applying your changes to your commandline, go ahead and click "Save" Next to your saved "MyServer" commandline, click "select." Now your server is set to restart with the new commandline. From here, go back to your "Game Services" panel and click "Restart" to restart your server. Once your server is rebooted, your admin password will have changed.
The last thing you need to do is to boot up your Project Zomboid client, and login to your server. Login with the default admin username, "admin" and the password as the password you set. Save your server and you will be able to log into an admin account with one click of your mouse.