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1) There are at least 3 implementations of ScreenConnect and this thread easily confuses them all. Automate, screenconnect.com (subdomain), and the adhoc client (subdomain of hostedrmm.com).

2) Having used these services in a MSP environment I know Automate will work with a headless machine no problem. The adhoc client I have not tested. screenconnect.com will have issues.

3) With screenconnect.com's agent, I was able to initially use the service and get into a headless PC. This PC has a ASUS B650E-E motherboard with onboard video and a GPU installed as well. Based on the default screen resolution of the window, it must be pulling the onboard video up. It has a glitch where most display changes related to Explorer will not update on the screen. For example if you click the start button, the menu will not appear. But if you click in the search bar, the window appears. If you right click on the task tray, you will see the options for Task Manager or Taskbar Settings (win11), but if you click on one of them, you won't see the window appear. Fix: send a CTRL + ALT + DEL after every request, hit esc to cancel, and the window refresh will appear. However, this won't work for right clicking task bar icons so you cannot unpin them. I ran into a UAC firewall issue, the screen locked up (no cursor or window updates including Ctrl + Alt + Del). So I rebooted. Now the mouse won't work so I can't get back into the machine. It takes me to the clock display, then I hit Ctrl + Alt + Del and it shows the login prompt, but I can't click into it to put a password. It appears that a ghost monitor device would be best. Will test with a monitor for now and see what happens.
Edit: hooking up a monitor fixed the GPU problem as expected. But mouse and keyboard was still unresponsive until I plugged in a mouse and keyboard.

Other notes: Remember to bypass consent, set power settings to not sleep, and disable UAC (if not on a domain).