ee.Image.arrayArgmax

// A function to print the array for a selected pixel in the following examples.
function sampArrImg(arrImg) {
  var point = ee.Geometry.Point([-121, 42]);
  return arrImg.sample(point, 500).first().get('array');
}

// Create a 1D array image.
var arrayImg1D = ee.Image([0, 1, 5, 2, 3, 4]).toArray();
print('1D array image (pixel)', sampArrImg(arrayImg1D));
// [0, 1, 5, 2, 3, 4]

// Get the position of the maximum value in a 1D array.
var maxValue1D = arrayImg1D.arrayArgmax();
print('Position of the maximum 1D array value', sampArrImg(maxValue1D));
// [2]

// Create a 2D 2x3 array image (reshape the 1D array image).
var arrayImg2D = arrayImg1D.arrayReshape(ee.Image([2, 3]).toArray(), 2);
print('2D 2x3 array image (pixel)', sampArrImg(arrayImg2D));
// [[0, 1, 5],
//  [2, 3, 4]]

// Get the position of the maximum value in a 2D array.
var maxValue2D = arrayImg2D.arrayArgmax();
print('Position of the maximum 2D array value', sampArrImg(maxValue2D));
// [0, 2]

# A function to print the array for a selected pixel in the following examples.
def samp_arr_img(arr_img):
  point = ee.Geometry.Point([-121, 42])
  return arr_img.sample(point, 500).first().get('array')

# Create a 1D array image.
array_img_1d = ee.Image([0, 1, 5, 2, 3, 4]).toArray()
print('1D array image (pixel):', samp_arr_img(array_img_1d).getInfo())
# [0, 1, 5, 2, 3, 4]

# Get the position of the maximum value in a 1D array.
max_value_1d = array_img_1d.arrayArgmax()
print(
    'Position of the maximum 1D array value:',
    samp_arr_img(max_value_1d).getInfo()
    )
# [2]

# Create a 2D 2x3 array image (reshape the 1D array image).
array_img_2d = array_img_1d.arrayReshape(ee.Image([2, 3]).toArray(), 2)
print('2D 2x3 array image (pixel):', samp_arr_img(array_img_2d).getInfo())
# [[0, 1, 5],
#  [2, 3, 4]]

# Get the position of the maximum value in a 2D array.
max_value_2d = array_img_2d.arrayArgmax()
print(
    'Position of the maximum 2D array value:',
    samp_arr_img(max_value_2d).getInfo()
)
# [0, 2]