On Amazon Linux 2 and PHP 7.4 I finally got PHP-ZIP to install and I hope it helps someone else - by the following (note the yum install command has extra common modules also included you may not need them all):
sudo yum -y install https://dl.fedoraproject.org/pub/epel/epel-release-latest-7.noarch.rpm
sudo yum -y install https://rpms.remirepo.net/enterprise/remi-release-7.rpm
sudo yum -y install yum-utils
sudo yum-config-manager --enable remi-php74
sudo yum update
sudo yum install php php-cli php-fpm php-mysqlnd php-zip php-devel php-gd php-mcrypt php-mbstring php-curl php-xml php-pear php-bcmath php-json
sudo pecl install zip
php --modules
sudo systemctl restart httpd