You will have to customize the ToolStripItem and obtain the rectangle in which the image lies using the ContentRectangle property.
Have a look at the ComputeImageAndTextLayout code sample on MSDN which calculates the rectangle in which the image lies.
In the MouseDown event of the ToolStripItem you will obtain the coordinates of the mouse in the ToolStripItem when the MouseDown event occurred as shown below
void item_MouseDown(object sender, MouseEventArgs e)
{
int x = e.X;
int y = e.Y;
}
You will then have to calculates if your MouseDown coordinates lies in the rectangle obtained and raise a ImageClicked event.
Using the same approach you could also raise a TextClicked event.