Most early choke heaters are designed to run on 6V, which is why they're wired to the alt. S terminal. I wouldn't be surprised if you found that yours is burned up (open circuit). And that wire doesn't turn the choke on - it only helps warm the choke spring faster to UN-choke the engine sooner. If everything else is working, the choke will still turn off, but it'll take a few extra minutes without a working choke heater.
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There's an active thread with a video of you & that off-road wrecker in the Chat forum.