Given the difficulty of figuring out exactly what the law says, and how most people have their own ideas about it, and the fact that the laws vary by jurisdiction, and that most people don’t even know what jurisdiction they are in at that crossing and probably don’t care, and the law leaves so much wiggle room, here’s how I would handle it:
Stop signs or signals. Make it very clear that one or the other party has the right of way, and must stop. No confusion.
That’s basically what the NPS has tried to do by posting stops and the infamous yellow sign anyway. We need to make it more clear. Either cars must stop, or peds/bikes, but somebody has to have the undisputed, constant right of way.
This whole thing has made me realize how much confusion there is and how confusion can be dangerous.
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