The most interesting best friend tag questions are the ones related to habits, personal traits and preferences, and situations the friends have been through. Being able to answer them correctly indicates they know each other well and value their shared memories.
A great way to come up with a habit question is by considering the different ways day-to-day actions can be performed. For instance, when they listen to music, do they like it loud or set it to a reasonable volume? When they walk on the street, do they maintain a fast pace or take their time? When in a conversation, do they spend the majority of their time talking or listening?
For traits, it's best to think mostly about words that could describe the friend. Are they introverted? Clever or adventurous? Disciplined, sensitive or moody? Virtually any characteristic can be used.
Personal preference questions can be very versatile too: What are their favourite color, animal, movie, band, place, or food?
Last but not least, there are questions about shared experiences and situations they've been through together. These questions can be either about remarkable memories and stories, such a day in which an interesting event took place, or related to moments important for their relationship, such as the day they met or first hung out with each other.