Unable to add a VLAN tag to a physical layer-3 interface.
Resolution
When a physical interface needs to be configured to handle VLANs, sub-interfaces need to be created (one per VLAN). The sub-interfaces are configured with the tag, and show as "tagged" when looking at the list of interfaces (see example), as opposed to the physical interface itself.
The example shows that ethernet1/4 remains untagged while its sub-interface (ethernet1/4.10) shows the VLAN tag ID.
Not being able to apply a VLAN ID on the physical interface is normal, expected behavior.