CNAME's with Cloudflare Tunnels

I have 2 domains that needs to point to the same webpage.
The first one is hosted/proxied within Cloudflare.
So I have setup a tunnel for the subdomain ping to my server.
But now I have another domain with name severs that I cannot change.
They created a CNAME record to
SO is configured to
But Cloudflare only gives an 404 error/blank page back on (not on, there the webpage is shown).
Is there a possibility to make it such that this works?

You might be able to do with locally configured tunnels, as I am not sure how much validation they do of if a hostname is in your account. I doubt it would work with remote tunnels.