How do I execute something WHILE something is happening?

Running a while loop without a wait can cause a game script timeout, even with a wait function, a while loop can cause yielding. Observe:

while true do
    wait(1)
    print('wow')--> a lot of wows
end;
print('potato')-- no potatos

Notice how as time goes on, the print function in the while loop always prints wow but never potato. Since the while loop has to repeat the code block, it will never go beyond.

A solution is to place the loop into a new thread, it is similar to making a new script and executing it without interrupting other scripts.

Functions like spawn or coroutine.wrap can make new threads. (note coroutine.wrap has a different way of placing code into a different thread)

spawn(function()
    while true do
        wait(1)
        print('wow')--> a lot of wows
    end;
end);
print('potato')-- potato

As I said in the comments, that is a For Loop not a While Loop

Loop Resource

To do this, you would use a While Loop, but also doing a Boolean Check.

Something like this, I would assume.

while wait() do
    if script.Parent.TopBar.Visible == true then
        script.Parent.ImageButton.Visible = true
        script.Parent.Forest.Visible = true
        script.Parent.Votes.Visible = true
    else
        script.Parent.ImageButton.Visible = false
        script.Parent.Forest.Visible = false
        script.Parent.Votes.Visible = false
    end
end

You would put this in a LocalScript inside of Intermission ScreenGui.

This will loop through the code every 0.03 seconds, checking if TopBar is visible. If TopBar is visible, it will make those 3 other elements visible as well. If it's not visible, then it will not have those 3 other elements visible.

To do your method, you would put a ServerScript in ServerScriptService and write this.

for _,player in pairs(game:GetService("Players"):GetChildren()) do
    while wait() do
        if player:WaitForChild("Intermission").TopBar.Visible == true then
            script.Parent.ImageButton.Visible = true
            script.Parent.Forest.Visible = true
            script.Parent.Votes.Visible = true
        else
            script.Parent.ImageButton.Visible = false
            script.Parent.Forest.Visible = false
            script.Parent.Votes.Visible = false
        end
    end
end

Either way really works. Both are efficient, I think?

Another way to do this is

script.Parent.TopBar:GetPropertyChangedSignal("Visible"):Connect(function(value)

But, this way would be easier as it's an always active loop. Refer to the Loop Resource for more information on loops.

Hope this helped! If this worked, let me know by selecting this as an answer!