there's not any difference in populating a drop down via a REST data source or any other.
Once the REST data source is defined you are good to go. This is explained here:
Regarding logs, where does it fail?
Does the test of the data source definition work in the Designer?
Otherwise you could check the following:
Enable diagnostic tracing from the avatar icon, load the Form, save the session and open the link with an admin user.
If you can use it in a path transition action you can take a look at the history, switch to admin mode an click on the action. You may be able to get additional information there. If you are using a rest action the whole request with body, headers and response will be logged. :)