I don’t understand what you mean by “good sales people will close before anything is signed” any good sales person will tell you that before you have money in the bank the client can still not pay they can even sign something and back out.
Obviously the difference is between 'customer has placed order' and 'customer will buy'. Great salespeople will use their energy and skill to achieve the latter with high probability of conversion. They do not need to hound the customer about signing/paying. They have closed and move to the next.
I'd advise you to get back into sales and learn it fully before giving advice here because if someone says they'll buy, you can't take it to the bank and cash it therefore you haven't made a sale. You need to make money and close, maybe that's the "killer instinct" you were talking about
