Ok, answers and clarification.
First off they are not talking about cider, it is badly written.. they are talking about cider vinegar or white wine vinegar, either one but not the drink known as cider.
The recipe is fine for a water bath, this is only used to expel air and fully seal the jars and thoroughly sterilise everything.
I would use firm pears, and use thick slices and I would follow the recipe but I would make sure that the pears didn't start falling apart. They shouldn't if firm enough to start. 10 minutes may be enough, it depends on the type of pear, so keep an eye on them. Don't overcook them.
I would then put onto hot scalded jars, cover with boiling syrup leaving 1'4 in headspace and process 500 ml for 15 minute..times starts after they come up to the boil.
Pears are high acid anyway so will be perfectly safe to store for ages if done this way. Just check the jars have sealed after they come out of the water bath, some may ping as you fill them but ignore that and process anyway.
Leaving them a month will concentrate the flavours.
Have fun. I am deep into processing today, I bought 10lbs of pears yesterday along same amount of beets, corn, apples , blueberries, rhubarb and peaches so I am slowly simking in jars !!
XX Jeannine
