Years of wear and a fault already on the dash is a common starting point for a service contract. The most useful thing to learn is how the contract treats that fault. Many contracts define a pre-existing condition and leave it out. That definition decides what the contract pays for, so read it before you talk about price.
What the clause usually does
A pre-existing condition clause generally says that a failure already present when the contract starts, or already known to the owner, is not covered. The wording varies. Some clauses look at the start date of the contract. Some look at the date of sale. Some look at what an inspection recorded. A few look at whether a warning light was on, or whether a repair was attempted before the contract began. Find the definition and read it in full, not the summary on the sales page.
The clause matters most on an older car because the car has had more time to develop faults. A fault that started before the contract may show up as a new breakdown after the contract starts. The contract may call that a continuation of an old condition and decline the claim. The owner may see it as a new problem. Ask how the contract decides which one it is. For the other side of this question, see how exclusionary and listed-parts contracts differ on older cars.
Say the fault out loud
If you already know about a problem, write it down before you sign. A noise, a leak, a light that comes on and goes off, or a repair that was never finished all count as things to name. Put it on the application, or ask the seller or the contract company how that item will be handled. Ask for the answer in writing. A verbal answer at the counter is hard to prove later.
Ask whether a repair before the contract starts changes the answer. Some contracts want a repair receipt. Some want a fresh inspection. Some do not change the answer at all. Get that rule in writing too.
Keep the paper
Keep every record that shows the car's condition at the start. That includes a pre-sale inspection report, photos of the dash, invoices from any shop that looked at the fault, and the diagnosis printout if one was made. These papers show when a condition was first noticed. Without them, the question of what was there at the start becomes one person's memory set against a clause.
Keep the sale paperwork as well. A bill of sale and the seller's written statement about known problems help show what the owner was told at purchase.
Questions to ask before you pay
Does the contract define pre-existing, and is that definition in the contract or on a separate page? Is the start date tied to the signing date, the sale date, or an inspection date? Does a fault seen on a pre-sale inspection count as pre-existing? Does a symptom that has not yet become a failure count? If a fault is excluded, will the contract name it in writing on the contract itself? Is there an inspection the company runs before it accepts the car, and who pays for it? If a claim is denied, what is the written reason, and how does the owner ask for a review?
Ask these of every company you compare. The answers will differ, and the differences are what the paper will do for you. This site does not say what any company's contract covers. Use the tables and the rubric for published figures, and read each contract for its own terms. For the mileage side of this question, see what changes for coverage at one hundred thousand miles.