No IP Tunnel usage

I have one domain working perfectly using tunnels. and another not working at all in the same tunnel.

I suspect, because the second domain does not have an A apex record, pointing at an IP.

Strangely, the working domain does have an A apex record pointing to an IP - but I have no clue where that IP address came from, nor what it is pointing to.

The working domain was a long-standing working domain transferred to Cloudflare from the original roster. - It has lots of DNS records, many A - pointing to 2 different IPs. I don’t know where these IPs came from.
The non-working domain was constructed in Cloudflare. I don’t have an IP to construct anA apex record. Creating a CNAME, pointing to the tunnel (as the documentation suggests) doesn’t work: Most often the error messages is “Cannot resolve domain”.

What I would like to do is simply use a tunnel to point to my local desktop server, without having an IP (Because I am in a shared office enviroment, with no control over the IP).
It’s working with one domain, and not the other.
Could anyone assist?