Thank you for pointing me in the right direction!
There is some additional settings that need to be in place as well, for those who come across this post later.
location ^~ /vhost1 { # https://nginxserveraddress/vhost1 (will take you here)
proxy_pass https://serveripaddr/ui;
proxy_http_version 1.1;
proxy_set_header Upgrade $http_upgrade;
proxy_set_header Connection "Upgrade";
proxy_read_timeout 86400;
proxy_set_header Host $host;
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Forwarded-Server $host;
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header Authorization "";
proxy_redirect off;
}
