You can register a frequently-used AF point to the camera. You can then use the Custom Controls menu to select either the 'Depth of Field' button or the lens' 'AF Stop' button (if the lens is so equipped - only Canon's Super Telephoto series of lenses have an 'AF Stop' button on the lens) to act as the [Switch to registered AF point] button. From page 108 of the Canon EOS 5D Mark IV Instruction Manual:

It appears that you, or someone else, has managed to set the point that you describe as "permanently flashing" as the 'Registered AF point'. It's only flashing in landscape orientation because you also have the menu option 'AF4 → Orientation linked AF point' set to either the second or third options that remember separate AF point settings for vertical and horizontal shooting. You don't appear to have selected a 'Registered AF point' for portrait orientation.

The 'Registered AF point' can be accidentally selected to the currently selected AF point if you are in one of the applicable AF selection modes (Single-point Spot AF, Single-point AF, AF point expansion - 4 points, AF point expansion - 8 points, or Automatic selection AF) and press the [light bulb] button on the top control panel while simultaneously holding down the [AF point selection] button.

How to set (or clear) the registered AF point is covered beginning on page 500 of the Canon EOS 5D Mark IV Instruction Manual.

To cancel a 'Registered AF point', hold down the [AF point selection] button at the upper right on the camera's back and press the [Flash Exposure Compensation/ISO] button on the top control panel.

The Custom Controls menu used to select the button that activates the registered AF point is covered beginning at page 495 of the Canon EOS 5D Mark IV Instruction Manual.