Service contracts are just another money changing scheme designed to separate you from your money. Their purpose is to be a "profit center" not a "cost center."
And, yes they are typically sold at point of sale.
That is so the (high) cost can be folded into the purchase price and financed.
There's a reason they don't offer monthly payments on the service contract policy...
Service contracts are typically provided by a 3rd party. Not the manufacturer of the product; some of the larger dealer groups had their own contracts. Don't know if that's still true.
Service contracts are always negotiable; be it for parts covered, time or mileage covered and of course price.
Service contracts are like any other insurance policies they can be obtained almost anytime, cost and coverage considered.