Half a gallon isn't actually a lot. It's a little bit underneath the amount you should be drinking daily, unless you are eating the recommended amount of fruits and vegetables, which most people don't.
I'm extremely athletic (I box among other things) so I'm a thirsty son of a gun and drink well over half a gallon, but I don't think it's benefited my tinnitus; sure helps my skin though.
The amount of water I consume on a given day has never affected my T in any way. That said,
according to the information posted by the Mayo Clinic, that's not a lot for an adult male or female.:
Every day you lose water through your breath, perspiration, urine and bowel movements. For your body to function properly, you must replenish its water supply by consuming beverages and foods that contain water.
So how much fluid does the average, healthy adult living in a temperate climate need? The National Academies of Sciences, Engineering, and Medicine determined that an adequate daily fluid intake is:
About 15.5 cups (3.7 liters) of fluids for men
About 11.5 cups (2.7 liters) of fluids a day for women
These recommendations cover fluids from water, other beverages and food. About 20 percent of daily fluid intake usually comes from food and the rest from drinks."