In Google Tag Manager, get a variable session storage. This is entered into GTM as "Customer JavaScript" variable. The result is also a variable as a "1st Party Cookie."

GTM_GetEmailFromSession.js

function ()
{
  	var result = '';
  
     if(typeof(Storage) !== 'undefined') 
    {
      
      	if (typeof(window.sessionStorage._enterCookieName) !== 'undefined')
        {
      		result = window.sessionStorage._enterCookieName + '';
        }
    } 
  	else 
    {
      	result = {{enter_1stPartyCookie_VariableType}};
    }   
  
  	return result;
}