Third-party apps such as Ecamm Live do not have the ability to set a YouTube Live broadcast's visibility status to Members only mode.
However, a Members Only broadcast can be conducted by following these steps:
1. Create your YouTube live broadcast as you normally would, either using Ecamm Live's scheduling feature, or using YouTube Studio.
2. Set the broadcast's visibility to Members only. To find this setting, go to the broadcast's live control room page, and then click EDIT. On the Edit settings screen, scroll down until you find the visibility settings, and pick Members only and then click DONE.
(Note that if you don't see a Members only option, this means that you do not have membership enabled for your channel.)
3. An important final step: Enable the broadcast's Auto-start setting. This will prevent Ecamm Live from inadvertently changing the broadcast's visibility to Public when the broadcast starts.