The z-space problem of displaying sprites

[icogil]

I wanted to make a sprite that follows a character like a visual equipment script without size restrictions, so I made the script below while studying and putting together several scripts for the past few days.
And the results were generally very satisfactory.

But one more problem arose.
If you adjust the z of the sprite created in this way, it will either go above everything on the screen, or below everything, and become invisible.
I honestly don't know what to do.
self.z I thought was the z value of the character's sprite.
It is not simply on top of the character sprite, but on top of the entire screen.
self.viewport.z also doesn't work
I also put it in viewport.z
I tried putting it in @_HEAD_sprite.z as well, but it doesn't work as I want.
What should I do?

current situation              what i want
                                

Code:

class Game_Character
  attr_accessor :sprite_HEAD
end



class Sprite_Character < Sprite_Character
  def create_HEAD_sprite(text)
   
    $game_variables[195]="Graphics/Characters/197-Support05"

    bitmap = Bitmap.new($game_variables[195])

    viewport = Viewport.new(self.x,self.y,bitmap.width/4,bitmap.height/4)
    viewport.z = self.z
    @_HEAD_sprite = Sprite.new(viewport)
    @_HEAD_sprite.bitmap = bitmap
    @_HEAD_sprite.ox = 0
    @_HEAD_sprite.oy = 0
    @_HEAD_sprite.x = self.x - bitmap.width/8
    @_HEAD_sprite.y = self.y - bitmap.height/8
    @_HEAD_sprite.z = self.z
    @_HEAD_sprite_visible = true

  end



  def dispose_HEAD_sprite
    @_HEAD_sprite.dispose
    @_HEAD_sprite_visible = false
  end

  def update_HEAD_sprite
    if @character.sprite_HEAD != nil

      if not @_HEAD_sprite_visible
        create_HEAD_sprite(@character.sprite_HEAD)
      end
     
      @_HEAD_sprite.viewport.rect.set(
      self.x-@_HEAD_sprite.bitmap.width/8,
      self.y-@_HEAD_sprite.bitmap.height/4,
      @_HEAD_sprite.bitmap.width/4,
      @_HEAD_sprite.bitmap.height/4)
      if @_HEAD_sprite.bitmap != $game_variables[195]
         @_HEAD_sprite.bitmap = Bitmap.new($game_variables[195])
      end

     
      @_HEAD_sprite.x = self.character.pattern * -@_HEAD_sprite.bitmap.width/4
      @_HEAD_sprite.y = (@character.direction - 2) / 2 * -@_HEAD_sprite.bitmap.height/4
      @_HEAD_sprite.viewport.z = self.viewport.z
    else
      if @_HEAD_sprite_visible
        dispose_HEAD_sprite
      end
    end
  end
    
  def update
    super
    update_HEAD_sprite
  end
end