local function AddContextMenuEntries(itemLink, itemID, inventorySlot)
  --zo_callLater(
    --function()
      MakeContextMenuEntry_AddItemToGearSet(itemLink, itemID)
      MakeContextMenuEntry_RemoveItemFromGearSet(itemLink, itemID)
      ShowMenu(inventorySlot)
    end
--, 10)
--end

local function AddContextMenuEntries(itemLink, itemID, inventorySlot)
  MakeContextMenuEntry_AddItemToGearSet(itemLink, itemID)
  MakeContextMenuEntry_RemoveItemFromGearSet(itemLink, itemID)
  ShowMenu(inventorySlot)
end
 
 
local function OverWriteInventoryShowContextMenuHandler()
  LibCustomMenu:RegisterContextMenu(
      function(inventorySlot, slotActions)
        -- Inventory slot should either be the player bag, equipment slots, or the bank.
        local slotTypesAllowed = {
          [SLOT_TYPE_ITEM] = true,
          [SLOT_TYPE_EQUIPMENT] = true,
          [SLOT_TYPE_BANK_ITEM] = true,
        }
        local slotType = ZO_InventorySlot_GetType(inventorySlot)
        if not slotTypesAllowed[slotType] then return end
        local bag, index = ZO_Inventory_GetBagAndIndex(inventorySlot)
        if not bag or not index then return end
        local itemLink = GetItemLink(bag, index)
        local itemID = Id64ToString(GetItemUniqueId(bag, index))
        if not itemLink or itemLink == "" or not itemID then return end
        easyDebug("Item ID of " .. itemLink .. ": " .. itemID)
        local itemType = GetItemLinkItemType(itemLink)
        local itemTypesAllowed = {
          [ITEMTYPE_ARMOR] = true,
          [ITEMTYPE_WEAPON] = true,
        }
        -- Item should be armor or weapon.
        if not itemTypesAllowed[itemType] then return end
        AddContextMenuEntries(itemLink, itemID, inventorySlot)
      end,
      LibCustomMenu.CATEGORY_LATE
    )
end

Added callbacks, you can register to, to hook into inventory slot context menu. You don't need to reinvent the hook and are able to control the position of your entry/entries more granular.

category
lib.CATEGORY_EARLY
lib.CATEGORY_PRIMARY
lib.CATEGORY_SECONDARY
lib.CATEGORY_TERTIARY
lib.CATEGORY_QUATERNARY
lib.CATEGORY_LATE

CATEGORY_EARLY is before the first built-in menu entry.
CATEGORY_PRIMARY is after the first built-in menu entry. And so on.
CATEGORY_LATE is after built-in menu and default.

lib:RegisterContextMenu(func, category)
Register to the context menu of the inventory mouse right click.

func: callback function to be called.
Signature:
Lua Code:
local function func(inventorySlot, slotActions)
end

category: optional. defaults to CATEGORY_LATE.

local function OverWriteInventoryShowContextMenuHandler()
LibCustomMenu:RegisterContextMenu(
          function(inventorySlot, slotActions)
            -- Inventory slot should either be the player bag, equipment slots, or the bank.
            local slotTypesAllowed = {
              [SLOT_TYPE_ITEM] = true,
              [SLOT_TYPE_EQUIPMENT] = true,
              [SLOT_TYPE_BANK_ITEM] = true,
            }
            local slotType = ZO_InventorySlot_GetType(inventorySlot)
            if not slotTypesAllowed[slotType] then return end
            local bag, index = ZO_Inventory_GetBagAndIndex(inventorySlot)
            if not bag or not index then return end
            local itemLink = GetItemLink(bag, index)
            local itemID = Id64ToString(GetItemUniqueId(bag, index))
            if not itemLink or itemLink == "" or not itemID then return end
            easyDebug("Item ID of " .. itemLink .. ": " .. itemID)
            local itemType = GetItemLinkItemType(itemLink)
            local itemTypesAllowed = {
              [ITEMTYPE_ARMOR] = true,
              [ITEMTYPE_WEAPON] = true,
            }
            -- Item should be armor or weapon.
            if not itemTypesAllowed[itemType] then return end
            AddContextMenuEntries(itemLink, itemID, inventorySlot)
          end,
          CATEGORY_LATE
  )
end

local function AddContextMenuEntries(itemLink, itemID, inventorySlot)
      MakeContextMenuEntry_AddItemToGearSet(itemLink, itemID)
      MakeContextMenuEntry_RemoveItemFromGearSet(itemLink, itemID)
      ShowMenu(inventorySlot)
end

--your code here
), delayInMilliseconds)