Prepare the veggies. Peel the cucumbers and slice into 3/4-inch coins or slice lengthwise into spears. Peel and thinly slice half of the onion, then finely chop the other half. Place the cucumbers, corn, jalapeno, onion and thyme in a heat-safe jar or sealable container.
Prepare the liquid. Heat the vinegar, honey, sugar, mustard, peppercorns, garlic, a nice pinch of salt and 1 cup water in a small pot on medium heat, stirring until the sugar and salt dissolve. Taste and adjust with more sugar or salt if needed. Bring to a simmer, then remove from the heat. Pour the hot liquid over the prepared veggies and stir. Cover and refrigerate until fully chilled. Serve chilled or room temperature.