Final answer:
The bulbourethral gland, also known as Cowper's gland, is responsible for providing the thin watery fluid that cleanses the urethra during ejaculation in a stallion.
Step-by-step explanation:
The accessory gland in the stallion that provides the thin watery fluid that cleanses the urethra during ejaculation is the bulbourethral gland, also known as Cowper's gland. This gland secretes a clear, alkaline fluid rich in proteins, which helps to lubricate the urethra and neutralize any urine that may remain, preparing it for the passage of semen. The release of the secretion from the bulbourethral glands typically occurs shortly after the male becomes sexually ar_oused and just before the release of semen, functioning as a preparatory phase for the safe and effective transfer of sperm.