Peel the sayote and slice into long pieces. Don't slice it too thin or the sayote will become limp and will not be crunchy. These were cut about a ⅓-inch thick. Transfer to a large bowl. If you have li hing mui, you can add these to the bowl, too.
Heat up white sugar, brown sugar, vinegar and Hawaiian sea salt on medium heat to form the syrup. Constantly stir the mixture and use clean and dry utensils. Make sure the pot and utensils aren't wet.
Pour the syrup into the bowl of sayote. With gloved hands, mix everything together so that the syrup is covering all the surface area of the sayote. The gloves will stop any contamination from your skin.
Optional: Add a few drops of red food coloring. This will give the pickled sayote that signature orange "pickled" look in a few days.
Transfer the sayote along with the the syrup into containers. If the sayote are floating above the syrup, place a small bowl or dish under the lid before you close it so that the pickling sauce is touching every slice.