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Hi and welcome to JustAnswer,Thank you for the question and your patience. Should you still need assistance for information purposes only...Initially, based on the above, the +12 on the white wire is present. Still, check for consistency; i.e. measure the white wire's +12V with ignition switch Off and then On.
If present and consistent, then for test purposes, jump the white wire and the gray wire. Note if +12 still present/consistent on both the white & gray wires. Attempt to start the Vulcan.
Repeat the above test between the white & brown wires.
Please post back results / observations of the above once tried.