You would have to add a bit more of the sentence to be absolutely sure but it seems here "on" means "in regards to" or "as far as... ...was concerned":
"In regards to 'when' the unauthorized structure was built, ...."
The actual use of on might be confusing because of the way the sentence is used. You only wrote half of the sentence so I imagine that the complete sentence is similar to the second one below:
"The girl was very courteous and smiled a lot when she left. However, on whether she would actually go out on a date with me, she was never quite clear."
We can rewrite the second sentence to get rid of the second comma and make it a bit more understandable:
"However, she was never quite clear on whether she would actually go out with me."