I would think you should drink when thirsty. As long as your fluids are calorically dense with some sodium in it to prevent washing yourself out it ought to help you bump your overall calories up too. It’s pretty hard to tell when thirst is coming from real thirst signals and when it’s excessive so I’d avoid chugging a lot at a time but not ignoring it either, no fun being thirsty all the time.
I drink whole milk and chocolate milk by the pint throughout the day with an occasional soda or glass of juice and my urine stays nicely concentrated (a total of 3/4 gallon to a gallon of fluid). I just hit 98.8 for the first time despite having already drank a quart of milk in the 2 hours since waking up so it seems to be working great for me.