Wash the pears, core them, chop them, and put in a large jar.
Add the thyme sprigs, the honey, and the sugar. Cover and shake the jar to combine the ingredients, then set aside for 2-3 days. Shake the jar a couple of times a day if you like.
After 2-3 days, the mixture should be juicy. Place a sieve over a large bowl and strain it. Don’t press the fruit the way you usually do; the pears (if ripe) are too soft for this and will drip large amounts of sediment into your shrub. Don’t even shake the sieve. (I did and managed to get a lot of sediment in the bowl, so I had to strain three times instead of twice!) Let time do the work.
Measure or eyeball the fruit-sugar mixture and add that much vinegar and a bit more.
Strain through a cocktail sieve into a jar or bottle; cover tightly and refrigerate until ready to use. You can try it now, but the flavors will meld, marry, and get happy over the next weeks.