How do I make the elseif work and the rotation from just changing the Y value only?

Since I've already solved the sound problem in the comments, I will go straight to the rotation problem.

If you want to make it so only the Y value changes, you can just use the tune part's X and Z values for the Rotation as the arguments for the new Vector3.

local tune = game.Workspace.Radio.Tune
sound = Instance.new("Sound", tune)
debounce = false

function onClicked()
    if not debounce then
    debounce = true
        tune.Rotation = Vector3.new(tune.Rotation.X, -69.598, tune.Rotation.Z)
        sound.SoundId = "rbxassetid://142295308"
        sound:Play()
    elseif debounce then
        sound:Stop()
        tune.Rotation = Vector3.new(tune.Rotation.X, -51.347, tune.Rotation.Z)
        sound.SoundId = "rbxassetid://209864226"
        sound:Play()
    elseif debounce then
        sound:Stop()
        tune.Rotation = Vector3.new(tune.Rotation.X, -89.282, tune.Rotation.Z)
        print("Off")
    debounce = false
    end
end

script.Parent.ClickDetector.MouseClick:connect(onClicked)

For your elseif problem, you've got two problems. The first one is that you never change debounce to false until line 20, which will never happen as line 11 will execute first, which is the second problem.

You can add to the other two if statements to check if the radio is on and the SoundId is equal to one of the SoundIDs and then run the different block of code like so:

local tune = game.Workspace.Radio.Tune
sound = Instance.new("Sound", tune)
debounce = false
radioOn = false

function onClicked()
	if debounce then return end --Stop the function if debounce is true.
	debounce = true
	if not radioOn then
		radioOn = true
		tune.Rotation = Vector3.new(tune.Rotation.X, -69.598, tune.Rotation.Z)
		sound.SoundId = "rbxassetid://142295308"
		sound:Play()
	elseif radioOn and sound.SoundId == "rbxassetid://142295308" then
		sound:Stop()
		tune.Rotation = Vector3.new(tune.Rotation.X, -51.347, tune.Rotation.Z)
		sound.SoundId = "rbxassetid://209864226"
		sound:Play()
	elseif radioOn and sound.SoundId == "rbxassetid://209864226" then
		radioOn = false
		sound:Stop()
		tune.Rotation = Vector3.new(tune.Rotation.X, -89.282, tune.Rotation.Z)
		print("Off")
	end
	debounce = false
end

script.Parent.ClickDetector.MouseClick:connect(onClicked)

I hope my answer helped you. If it did, be sure to accept it.