Use the remote user to map users not defined in Local login.
This could be better explained in the documentation. Let's use two clear terms just for this answer to avoid confusion.
Local server = Where you are creating a linked server
Remote server = Server you are connecting with Linked Server
Local Login = Can be SQL authentication or Windows ...
RLS does not have a way to react to accesses of inaccessible content. Throwing an error would disclose the existence of the inaccessible object, an information disclosure vulnerability susceptible to guessing attacks. Logging is a little less so, although if the log file metadata is viewable then a similar attack is possible.
For auditing accesses for ...