I have created a custom entity type (without bundles) using the Drupal Console command. Everything works fine with the out the box stuff. I can configure fields, the order of the form and the order of the output display.
However, it seems impossible to add and new View Modes to my new entity type. I have tried adding a new mode to the "Content" view modes section but I don't have the collapsable details section to be able to enable new view modes.
Is there a setting I have missed in the entity code that will display this?
/admin/structure/display-modes/view/add
, unless you also explicitly create at least one view mode programmatically for that entity (see @Jimmyb_1991's answer below). After at least one view mode exists, additional view modes can be added using the UI.