If they still owe $12,800 on it, they will not settle for less. That is just human nature. Waiting them out with time will not work. Even if they make another couple monthly payments, the balance will still be $12,500 or more.
But, buying from a private seller will save you sales tax. At 7%, that is a $900 savings over buying from a dealer. That makes the $12,800 out the door price about even with buying it for discounted at $12,000 and then paying sales tax. $12,800 out the door sounds good.
Since it is being financed, make sure that the check you write is payable to the buyer AND the company financing it. Otherwise, their lender still has a legal claim on the tractor. I would be shocked if the lender did not have a security interest in the tractor and loader with serial numbers recorded. If the seller gives you a simple bill of sale and runs with your money, you MIGHT, depending upon the state, still be in jeopardy of the lender reposessing the machine once payments stop being made to the lender.
Do not allow yourself to get into a position where you pay the seller $12,800 and then have to make all the rest of the payments too. Your 790 would become a $25,000 tractor!!!!!!! No honest seller is going to mind having the check written to them AND the lender. This way, you have the peace of mind that the sale is legal and final. They have already told you they owe on it, so they can't suddenly say there is no lender to pay off. The last thing you need is for them to go spend the $12,800 and not pay off their loan.
Since they are selling the tractor, I will guess they may also have a bunch of accessories that they will no longer need. Ask what other stuff gets thrown in. They may have grease guns, a case of diesel oil, extra filters, etc. all those items could sweeten the pot by a couple hundred dollars.