Ok so you can try allowing HEAD Requests from only Uptimerobot IP addresses/host servers. If that does not work then you would need to allow all HEAD Requests. Whitelisting Multiple Uptimerobot IP address would be done like this:
RewriteCond %{REMOTE_ADDR} !^(xxx.xxx.[0-9]{1,3}.[0-9]{1,3}|xxx.xxx.[0-9]{1,3}.[0-9]{1,3}|xxx.xxx.[0-9]{1,3}.[0-9]{1,3})$
Or using this condensed condition:
RewriteCond %{REMOTE_ADDR} !^(xxx.xxx.|xxx.xxx.|xxx.xxx.)[0-9]{1,3}.[0-9]{1,3}$
Uptime Robot IPv4 and IPv6 IP addresses:
# Uptime Robot IPv6 IP addresses
RewriteCond %{REMOTE_ADDR} !^(2604:a880[:\d\w]+|2607:ff68:107[:\d\w]+|2a03:b0c0[:\d\w]+)$ [NC]
# Uptime Robot IPv4 IP addresses
RewriteCond %{REMOTE_ADDR} !^(216.144.|69.162.|63.143.|46.137.|46.101.|122.248.|188.226.|178.62.|54.79.|54.94.|54.67.|54.64.|104.131.|159.203.)[0-9]{1,3}.[0-9]{1,3}$