Just to rule that out. You don't use port 46 for the ESXi host, do you? It's not tagged for VLAN 12.
Anyway, since the newly created VLAN 11 also doesn't seem to work, I think you may need to take a closer look at the router which - from what I understand - is your pfSense.
Another option would be to configure one of the physical switch ports as untagged for VLAN 12, and connect e.g. a notebook to see whether this gets network access.
André