It is used by women to indicate their awareness of their 'child bearing' years. 'My biological clock is ticking' for example is a common phrase used by women or prospective parents. But it also refers to our life cycles and changes in our bodies during our lifespan for both men and women. You would not use it to describe yourself as a morning person as in your example.

When used in everyday conversation, it’s used as others have said: to refer to awareness of child bearing years. In scientific use, it can be used to describe any time-based cycle of an organism. In this case, you could use it to describe a wake/sleep cycle. Stick with “body clock” for everyday use to describe night/morning person.

Good question! "Biological clock (is ticking)" is used for women who feel a need to have children before they are too old. When you take a long-distance flight and your sleep cycle is disrupted, you could say: "My body clock is 5 hours behind" "My body clock is out of sync" We do not use these for "night person / morning person". For these meanings you can use: "I'm a night owl" "Are you more of an owl or a lark"? "Night owl" for "night person" is much more commonly used than "lark" for "morning person".

Daughter, 24 and not married. You know your biological clock is ticking. Not usually used to describe night and morning people. She's a bit of a night owl. She's not a morning person. . I woke at 3AM, I think my biological clock is still on Beijing time. <-- not so common. I woke at 3AM, I think I'm still on Beijing time. <-- more common. . You could also look for circadian clock/cycle, but not really a daily use phrase.