In Japan, when making a deeper or more formal bow, it is not normal to keep looking directly into the other person’s eyes while your head is lowered. As your upper body moves forward, your gaze naturally drops as well.
That does not mean there is a simple rule that says you should never make eye contact while bowing.
When greeting someone, you normally look at them first. If you are making a deeper or more formal bow, your gaze lowers as your upper body bends forward. When you straighten up again, you look at the other person once more.
In other words:
Look at the person → greet them → lower your gaze as you bow → look at them again when you straighten up.
If someone bends forward but keeps their face tilted up to maintain eye contact, it tends to look strange rather than rude. With a deeper bow, keeping your eyes fixed on the other person’s face simply does not match the movement of the body.
A small everyday nod or slight bow is different.
If you are only dipping your head briefly while passing someone or giving a casual greeting, it is perfectly normal to keep looking at the other person. The movement is so small that there is no need to deliberately lower your gaze.
With a more formal bow in a business setting, apology, or other serious situation, however, the deeper your upper body bends, the more natural it is for your gaze to drop with it.
Foreign visitors do not need to memorize exact bowing angles or where their eyes should be at every moment.
With a slight bow, keeping eye contact can be completely natural. With a deeper bow, let your gaze drop naturally as you bow.
That distinction is enough.
