Selecting a monitor down the virtual server & pool

That would suggest that your bigip is unable to reach the pool members.

Note that in a cluster, while load balanced end user traffic goes through the floating IP, health checks are sent by the local-only IPs of each individual cluster member.

So if there's a firewall, make sure all bigip IPs are allowed.

If that's not it, you can use something like curl directly on the bigip CLI to see what kind of response you get from the pool members, if any.

But that's more interesting for failing http(s) checks. The basic TCP health check failing points towards a very fundamental connectivity issue, like routing, firewall, access list or the service not even running on the pool member.