I would like to daemonize the answer in this topic https://serverfault.com/a/480871/94127. Since varnishlog has daemon mode, I tried to use -D option as below. But the timestamps are not appearing.
varnishlog -I "Back healthy|Went sick" -w /var/log/varnish_health.log -D | awk '{ print strftime(), $0; fflush()}'