Target Display Mode won't Work

Have you tired the troubleshooting steps in the article on Target Display Mode:

Use your iMac as a display with Target Display Mode - Apple Support

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Troubleshooting Target Display Mode

Here's what I tried and what finally worked.

• Confirmed “Target Display Mode” was available for my iMac 27-inch “Core i5” 2.7GHz (Mid-2011).
• Confirmed “Target Display Mode” should work for macOS High Sierra or lower.
• NOTE: My iMac runs High Sierra and will not run macOS any more recent.
• Pressed “Command-F2” using Logitech keyboard model K360. Failed.
• Sent “Command-F2” via AppleScript:
  • “tell application "System Events" to key code 144 using command down”
  • “tell application "System Events" to key code 120 using command down”
  • Both failed.
• Pressed “Command-F2” using Apple keyboard model A1048, which is a wired keyboard. Failed.
• Checked Thunderbolt 3 to Thunderbolt 2 adapter and Thunderbolt cable by inspecting and noting a "device" was connected via: About this iMac —> System Report —> Hardware —> Thunderbolt
• Pressed “Command-F2” using the Apple aluminum wireless keyboard that comes with the iMac out of the box.
• THIS IS WHAT WORKED.

If that hadn't worked, this was what was next:

• Try: Different Thunderbolt cable
• Try: Different Thunderbolt 2 to Thunderbolt 3 adapter
• Try: Dropping to macOS Sierra
• Try: Dropping to OS X El Capitan
• Try: Dropping to OS X Yosemite
• Try: Dropping to OS X Mavericks