Why is my SQL profiler not registering any events from SQL Express when running under Administrator?

Some application needs to perform an elevated operation, during which it fails to read a record from a table in MS SQL Express, which is working fine under the regular user. I wanted to run a trace and see what is failing, but the trace is failing as well.

First, I stopped the SQL Express instance that runs under the current user who had launched the application: SqlLocalDB.exe stop, and then I checked in the task manager that there were no more sqlserver.exe instances running.

Next, I started SQL Profiler under Administrator, and it automatically started its own instance under Administrator as well. But when I either launch the application or run SSMS under Administrator, the still running trace shows no new entries. Only when everything is running under the regular user do I see new entries in the trace. What am I doing wrong, and should it not work just as well when everything is running under the Administrator?