"Attempt to index nil with PlayerGui"?

The Attempt to index with exception refers to the trailing Instance, not the Instance of query. Therefore, there is an issue with the Player; the only scenario where LocalPlayer would be invalid is a ServerScript.

It is a common mistake many beginners make, as they're unaware of basic networking logic. A Server, is a mainframe that manages multitudes of Clients, and is not a Client itself. The LocalPlayer refers to the Player Object affiliated with the local machine; as aforementioned, a Server isn't a connected user, which is why we cannot allocate a Player Object from it.

The primitive difference between a LocalScript and a Script, is that each variation of the program is designed to run on it's respective end... LocalScripts will be ran via the ROBLOX Player on the user's device, whilst a Script will be ran on the ROBLOX Server.

This is why we can denote a Player Object through a LocalScript, as the program resides within the local machine

Though, we can still achieve your goal, just through a different approach. A Sever can still understand what Clients are connected, and what are connecting. We can catch a connecting user through the .PlayerAdded signal of the Players Service. From here, we can modify their User Interface:

local Players = game:GetService("Players")

local function EnablePlayerGui(Player)
    local PlayerGui = Player:WaitForChild("PlayerGui")
    local THBTMA = PlayerGui:WaitForChild("THBTMA")
    THBTMA.Enabled = true
end

Players.PlayerAdded:Connect(EnablePlayerGui)

You need to use :WaitForChild() in order to make the script wait for the PlayerGui object to be created on the player

game.Workspace.sFX.TimeHasBegunToMoveAgain:Play()
game.Players.LocalPlayer:WaitForChild('PlayerGui').THBTMA.Enabled = true
wait (3)
game.Players.LocalPlayer:WaitForChild('PlayerGui').THBTMA.Enabled = false