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Sorry I just saw this! Maybe I'm not explaining correctly (or maybe I've got some old settings since we've been using the product for a few years). All of my computers are domain joined and Access sessions. I don't need to elevate on connection, but I usually need to elevate during the session to complete administrative tasks for example:

User contacts service desk, needs software installed. Service desk connects to user's computer (to their active session). Service desk opens an EXE to install software. Windows UAC pops up. Service desk needs to elevate to install software. Currently, they need to look up the LAPS information to do this, but if Control was able to look up the LAPS password (from the toolbar?) and auto enter that would be awesome!