Attempting to set the TailVisible property of a BubbleChatMessageProperties instance will do completely nothing at all.
If the BubbleChatConfiguration’s TailVisible property is set to true and the BubbleChatMessageProperties overwrites it to false for a message, it will still remain as true in the end result. The same thing happens otherwise if originally false set to true, nothing changes.
The code sample below is exactly what I used for testing, and I manually changed the TailVisible of TextChatService.BubbleChatConfiguration prior to each test.
local TextChatService = game:GetService("TextChatService")
TextChatService.OnBubbleAdded = function(message: TextChatMessage, adornee)
local properties = Instance.new("BubbleChatMessageProperties")
properties.BackgroundColor3 = Color3.fromRGB(0, 0, 0) -- This works
properties.TextColor3 = Color3.fromRGB(255, 255, 0) -- This works
properties.TextSize = 20 -- This works
properties.TailVisible = false -- DOESN'T work regardless of if true | false.
print(properties.TailVisible)
return properties
end

