Under the covers, creating an event source requires writing to the HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\EventLog
registry key, which is only writable by administrative users. Thus, any API built on top of this is going to require elevated permissions. Creating the event source would be something you would need to do after elevation.
But once you have created the event source, actually reporting an event does not require elevated permissions. If you could run an installer, your installer could request elevation and create the event source; and then your application just report events as any other application would. But I think this is kind of a no-go situation in a logon script.