Find index number of display shown in the OS's display settings. The reliability of this method is unknown.

DisplayHelper.cs

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Runtime.InteropServices;
using System.Text;

public static class DisplayHelper
{
    #region Win32

    [DllImport("Setupapi.dll", SetLastError = true)]
    private static extern IntPtr SetupDiGetClassDevs(
        [MarshalAs(UnmanagedType.LPStruct), In] Guid ClassGuid,
        IntPtr Enumerator, // Null
        IntPtr hwndParent, // Null
        DIGCF Flags);

    private const int INVALID_HANDLE_VALUE = -1;
    private const int ERROR_NO_MORE_ITEMS = 259;

    [DllImport("Setupapi.dll", SetLastError = true)]
    [return: MarshalAs(UnmanagedType.Bool)]
    private static extern bool SetupDiDestroyDeviceInfoList(
        IntPtr DeviceInfoSet);

    [DllImport("Setupapi.dll", SetLastError = true)]
    [return: MarshalAs(UnmanagedType.Bool)]
    private static extern bool SetupDiEnumDeviceInfo(
        IntPtr DeviceInfoSet,
        uint MemberIndex,
        ref SP_DEVINFO_DATA DeviceInfoData);

    [DllImport("Setupapi.dll", CharSet = CharSet.Auto, SetLastError = true)]
    [return: MarshalAs(UnmanagedType.Bool)]
    private static extern bool SetupDiGetDeviceInstanceId(
        IntPtr DeviceInfoSet,
        ref SP_DEVINFO_DATA DeviceInfoData,
        [Out] StringBuilder DeviceInstanceId,
        uint DeviceInstanceIdSize,
        out uint RequiredSize);

    [StructLayout(LayoutKind.Sequential)]
    private struct SP_DEVINFO_DATA
    {
        public uint cbSize;
        public Guid ClassGuid;
        public uint DevInst;
        public IntPtr Reserved;
    }

    [Flags]
    private enum DIGCF : uint
    {
        DIGCF_DEFAULT = 0x00000001, // only valid with DIGCF_DEVICEINTERFACE
        DIGCF_PRESENT = 0x00000002,
        DIGCF_ALLCLASSES = 0x00000004,
        DIGCF_PROFILE = 0x00000008,
        DIGCF_DEVICEINTERFACE = 0x00000010
    }

    #endregion

    /// <summary>
    /// Finds index number of display shown in the OS's display settings.
    /// </summary>
    /// <param name="deviceInstanceId">Device instance ID</param>
    /// <returns>If found, one-based index number. Otherwise, -1.</returns>
    public static int FindIndexOf(string deviceInstanceId)
    {
        var ids = EnumerateMonitorDeviceInstanceIds()
            .Reverse()
            .Select((id, index) => (id, index))
            .ToDictionary(x => x.id, x => x.index + 1);

        return ids.TryGetValue(deviceInstanceId.ToUpper(), out int index)
            ? index
            : -1;
    }

    private static readonly Guid GUID_DEVINTERFACE_MONITOR = new Guid("E6F07B5F-EE97-4a90-B076-33F57BF4EAA7");

    private static IEnumerable<string> EnumerateMonitorDeviceInstanceIds()
    {
        var deviceInfoSet = IntPtr.Zero;
        try
        {
            deviceInfoSet = SetupDiGetClassDevs(
                GUID_DEVINTERFACE_MONITOR,
                IntPtr.Zero, // DISPLAY
                IntPtr.Zero,
                DIGCF.DIGCF_DEVICEINTERFACE | DIGCF.DIGCF_PRESENT);
            if (deviceInfoSet.ToInt64() == INVALID_HANDLE_VALUE) // Assuming 32bit process
            {
                Debug.WriteLine($"Failed to get device information list.");
                yield break;
            }

            uint memberIndex = 0;

            while (true)
            {
                var deviceInfoData = new SP_DEVINFO_DATA { cbSize = (uint)Marshal.SizeOf<SP_DEVINFO_DATA>() };

                if (SetupDiEnumDeviceInfo(
                    deviceInfoSet,
                    memberIndex,
                    ref deviceInfoData))
                {
                    yield return GetDeviceInstanceId(deviceInfoSet, deviceInfoData);
                }
                else
                {
                    if (Marshal.GetLastWin32Error() == ERROR_NO_MORE_ITEMS)
                        yield break;

                    Debug.WriteLine($"Failed to enumerate device information structures.");
                }
                memberIndex++;
            }
        }
        finally
        {
            SetupDiDestroyDeviceInfoList(deviceInfoSet);
        }
    }

    private static string GetDeviceInstanceId(IntPtr DeviceInfoSet, SP_DEVINFO_DATA DeviceInfoData)
    {
        SetupDiGetDeviceInstanceId(
            DeviceInfoSet,
            ref DeviceInfoData,
            null,
            0,
            out uint requiredSize);

        var buffer = new StringBuilder((int)requiredSize);

        if (SetupDiGetDeviceInstanceId(
            DeviceInfoSet,
            ref DeviceInfoData,
            buffer,
            requiredSize,
            out _))
        {
            return buffer.ToString();
        }
        return string.Empty;
    }
}