Hello Matt,
Thank you for your comment.
I can install Teamviewer Full (with Unattended access) on a Terminal Server and get a Teamviewer ID that gets me to the 'console'.
I haven't tried that (intalling TV for the console access), but I looked at the hypothesis that Remote Desktop could be involved in the double TV ID. I have tried uninstalling TV and reinstalling it either from Remote Desktop connection or from direct access to the computer; and I tried stopping TV processes and restarting them either from Remote Desktop or from direct connection to the computer. I have seen no difference. (I used Remote Desktop to connect as a 'normal' user though, not to connect to the console like you mentioned.)
But in the process of doing that, I realized that TV has one ID if it starts automatically with Windows, and it has another one if it is started by a user. So if the computer is rebooted, TV will have one ID and if for some reason, the process is restarted by an user, it will have another ID. The ID that TV takes when it starts automatically with windows is the 'new' one (i.e. the one that appeared recently).
Does that seem normal or should I be worried about a security problem (something malicious somehow changing TV ID at boot time)?
Best,
Frederic