I have no reason to doubt that you'll choose the time randomly, but there's a way to prove your integrity in that choice beyond all doubt, with just a bit of hassle:
Pick a time now, follow it with a random salt, save it somewhere you'll remember, and then comment with the SHA-256 of it.
For instance, I could pick 2:47 PM, pick some random words and privately save the string "2:47 PM umbrella support imitation", input that into an online SHA-256 calculator, and then comment here with the output "6e83b5e6f8121ee27826971d548927d0df0094b18b3269d26e23db9cdaaa1d15". (Commenting is better than putting it in the description because you'll have no reason to edit the comment, so it'll show that you never edited it.)
That way when you resolve the market, you can reveal the original string and make it perfectly verifiable that you chose your random time well in advance!