BA rules, interesting.
These are the only references i could find on the ba.com site in regards to stopovers:
13.8. There are no charges for stopovers included in an Award itinerary. Where stopovers are at connecting points on the most direct route between origin and destination.
Rules seem thin on their website. Seems like you can stopover at any place you want, along the route for as long as you want, so long as it is what they consider along the "most direct route".
How do you know if LAX-NRT-HKG-KLL is considered a most direct route?
If the airline offers NRT-KLL, does that consider NRT-HKG-KLL (stop in HKG) an indirect route? Hmmm.