GUI Jump Button: When clicked, nothing happens?

Not sure why they will not jump. You can try to use a RemoteEvent instead. On the server side, listen for the OnServerEvent event, and on the client side call :FireServer().

local debounces = {} -- # list of debounces so player does not spam

-- # remember to define remoteEvent
remoteEvent.OnServerEvent:Connect(function(client, request)
    if request == "jump" and not debounces[client] then -- # they requested to jump, and are not in the debounces table
        debounces[client] = true
        client.Character.Humanoid.Jump = true
        wait(2)
        debounces[client] = nil
    end
end)

And from the local script

local button = script.Parent -- # localise variables
local isMobile = game:GetService('UserInputService').TouchEnabled
button.Visible = isMobile -- # TouchEnabled holds a boolean value. Just set the visibility to that boolean!

local function jump()
    remoteEvent:FireServer("jump") -- # remember to define remoteEvent
end

button.Activated:Connect(jump)
-- # Activated is the recommended way of listening for GUI button clicks

Also TouchEnabled should not be the only way to determine if the player is on mobile or not. What if a user has a touch screen computer? You can use MouseEnabled and KeyboardEnabled in addition to TouchEnabled. As well as other checks.

So while Incappax is right that you need to use Remote Events, the following can just be placed into the script without writing extra lines of code.

Local Script

local button = script.Parent
local mobile = game:GetService('UserInputService').TouchEnabled
local remote = game.ReplicatedStorage.Jumping

if mobile == true then
    button.Visible = true
end

function jump()
    remote:FireServer()
end

button.Activated:Connect(jump)

Server Script

local remote = game.ReplicatedStorage.Jumping

remote.OnServerEvent:Connect(function(player)
    local char = game.Workspace:FindFirstChild(player.Name)
    if char ~= nil then
    char.Humanoid.Jump = true
    end
end)

You can also a debounce with a wait time to prevent further use of the button until the player stops jumping.

Local Script with Debounce:

local button = script.Parent
local mobile = game:GetService('UserInputService').TouchEnabled
local remote = game.ReplicatedStorage.Jumping
local debounce = true
local player = game.Players.LocalPlayer

if mobile == true then
    button.Visible = true
end

function jump()
if debounce == false then return end
debounce = false
    remote:FireServer()
    repeat wait() until player.Character.Humanoid.Jump == false
debounce = true
end

button.Activated:Connect(jump)