Add Google Tag Manager to wp-login.php

I am using the wp-login.php for my user login page. I am trying to add in the Google Tag Manager code into the body of the wp-login.php. It needs to go after the opening body tag, however, all the hooks I use only can add code inside the head tag – which won’t work for Tag Manager code. How can I hook the Tag Manager code in the body of the wp-login.php page? I am currently using:

add_action( 'login_head', 'synt_ga_login_page');
function synt_ga_login_page() { ?>

Inside the function file. But that puts the code inside the head tag. I need to place it into the body tag. Can anyone offer help on this?