A few things after reading your question, some of the comments, and your comments back and forth to and from others. I'm posting some detail and then a potential solution at the bottom which I've confirmed worked fine in a test/lab environment a while back. I encourage you to read over my answer entirely as there are some gotchas, etc.
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How to stop remote desktop logoff after closing the connection
For this question above, others have answered and suggested the GPO settings—"idle and disconnected session time limits to unlimited"—to look over and ensure that the user disconnects rather than logoff.
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I am logging to the currently active user. It still presents them with
the lock-screen as soon as I log in. Tested on 2 comps physically next
to each other, so visual examination from both sides is simple. This
has been since possibly XP, definitely 7 & continues on 10. I'd love
to be able to do it interactively, like I can with Apple's Remote
Desktop or even TeamViewer.
Notable Items
Using TeamViewer on Windows will still not allow multiple or concurrent RDP sessions on a Windows non-Server OS. It will allow
you to interact with currently existing RDP sessions or active
console sessions only. If you do not have more than one of those
to connect to for interacting with, it'll not give you the expected
result.
Microsoft sells Server OSes and Client Access Licenses for Terminal
Server access with a cost associated per user or per device CAL as
I've seen others mention in comments, answers, etc. So for Microsoft
non-Server OSes, they leave this Terminal Server RDP-expanded
functionality not enabled or disabled for that reason.
Microsoft Server OSes can usually handle more concurrent RDP sessions
more efficient on the same machine with more memory support. They also don't have as much Microsoft built-in
features and functions enabled by default. Non-Server Windows OSes may
have to be configured explicitly disabling unnecessary things from running by default optimizing performance.
The Potential Workaround
Warning: I suggest doing this in only a test or lab environment for testing purposes only, so I'm not suggesting to use this for
production purposes in a business environment. Otherwise, use with
caution and at your own risk since I have no idea about the legalities
of using this long-term for such purposes.
Referenced below is a link to a source called RDPWrap which is on GitHub that is a free download. Posted there are full instructions with screen shots for visuals on the site including step-by-step detail—it is only trivial to figure out and get it tested.
To download you need the actual install file rather than the non-compiled source code, from the below link named RDPWrap Install File Download Link in the Download section of that page. Just click on the link named RDPWrap-v1.6.zip to download the EXE and batch install files contained within this ZIP file (screen shot below).
Gotchas
If you apply Windows Updates on one of your test machines and this functionality ends up not working afterwards, you may need to run the install again to patch over the files, etc. You may also need to check the source GitHub resources for other bug patches within new releases since this is something someone else provides and Windows OSes should apply Windows Updates for security reasons.
Important: Domain level Group Policy and/or Security Policy settings may override all the below listed local Registry, local Group Policy, and local Security Policy settings. From what I can tell but not confirm myself, ensuring these settings are set as specified will prevent disconnected RDP sessions from being logged off after a certain period of time. You may need to reboot the machine after making any local settings changed below for those to become effective. You may need to check for domain level Group Policy or Security Policy settings that take precedence over the local settings if you still have trouble after ensuring these settings are set locally per machine.
Change these registry values as shown in the screen shot to enable or disable the ability to allow more than one concurrent RDP session with the SAME account. You'll need to change and/or create this key manually perhaps and set per each run of the RDPWrap patch software on your test systems.
To change this setting, you'll need to perform a registry change. The
following steps describe the process:
Start Registry Editor (by default, this is located at
c:\windows\regedit.exe).
Go to the following registry key:
HKEY_LOCAL_MACHINE\System\CurrentControlSet\Control\TerminalServer
If the fSingleSessionPerUser value doesn't exist, create a new DWORD
value named fSingleSessionPerUser
Open the fSingleSessionPerUser value. The possible values for this
setting are as follows:
0x0
Allow multiple sessions per user
0x1
Force each user to a single session
- Enter the new setting, and then click OK.
A. From GPEDIT.MSC ALL the below settings in both Computer Configuration and User Configuration need to be set to a State of Not configured.
These Group Policy settings are located in the following locations:
Computer Configuration\Policies\Administrative Templates\Windows Components\Remote Desktop Services\Remote Desktop Session Host\Session Time Limits
User Configuration\Policies\Administrative Templates\Windows Components\Remote Desktop Services\Remote Desktop Session Host\Session Time Limits

B. From SECPOL.MSC the below (screen shot highlighted) setting in Interactive logon: Do not require CTRL+ALT+DEL needs to be set to a Enabled.
1. Local Policies\Security Options

Download Link Screen Shot

Sources: