Hi Sherlock,
Have you already disclosed your issues with your boss? Do you have a formal diagnosis of your troubles? If you haven't disclosed yet, and you have a formal diagnosis, then it might be time to disclose. If you're having a difficult enough time that you're considering quitting then you have less to lose. You might as well see if you can get help.
I say that now is probably a good time to disclose partially because the way you describe it it's not so much that you just got in big trouble and are making excuses for the trouble, but that you're having all around difficulties and need to address those. Disclosing after some major event could seem like you're making excuses for the event so it's good that you seem to be being proactive. (I am not sure if this paragraph makes sense, but if it doesn't let me know and I'll try to clarify).
Then once you explain that you have difficulties try to share with your leader what they can do to help. As I read your message it sounds like you're not receiving complete instructions. NT leaders are likely to assume, and to try to respect, that people understand what "chatting to the customers" means. However, that statement seems very confusing and vague if you ask me. Ask your boss for advice on the kinds of questions and topics that you might want to talk with customers about. This way you can collect a list, sort of like having a script.
After all, the worst thing that could go wrong if you disclose and ask for better instructions is that you could get fired... but if they fire you for that then that is a touchy issue on their end. Also you're already considering quitting in the first place so maybe separating from the job isn't the worst thing.
The advice above about lining up another job is sound though. It might make sense to see what's available and if you think you could quickly land an alternative job if you were to get fired or decide to quit after all.
My summary advice: Try drastic things before giving up 
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Very high systematizing, low empathy, but moderate to high sympathy.
I do not experience cognitive dissonance reduction the way that other people do.
Professionally diagnosed in March 2018