.... What is the + 12 wire though?
+12v to the lightbar switch is usually done by tapping into the headlight wire at 'A' in the diagram below. Since you said your headlights work it follows you should have electricity at the switch. If you don't, I suspect that the vampire tap on the headlight wire is faulty. For now, you don't have to know what the headlight wire looks like. You can trace back the +12 wire from the lightbar switch, or look up the schemetic for the color of the headlight wire (R=red R/W=red wire with white stripe, etc).
The switch's outbound wire at 'B' doesn't (or shouldn't) go to the auxiliary lights. Instead the electricity is routed to an intermidiary 'relay.' [ A relay is an electro-magnet switch .... when electricity is sent to the relay, the electro magnet switch turns ON, and so forth.] With the relay in its ON state, electricity now flows from the battery to the auxiliary lights. *I suggest you check the inline fuse (red box).* It should be on one or the other side of the relay.

Perhaps, you should ask the PO whether ....
he used a relay? (see footnote, below)
if so, did he splice in an inline fuse?
which wire did he tap into to power the lightbar switch?
It might be a simple thing like both light bulbs went out at the same time. Best wishes.
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*the below is meant more for rxvalk*
The reason that an intermidiary relay is necessary, is that the current for the headlight flows through the Start Button with the factory configuration. If you were to feed the headlight current directly to the auxiliary lights, the combined amp draw would eventually melt the nylon substrate in the start button. Start buttons aren't sold separately. You would have to purchase the entire right side housing to get a new start button. Thusly, relays are cheaper. The start button in this context is a known weak point on practically all bikes, not just on Honda's.
The headlight wire is usually tapped because it's conveniently nearby the lightbars. But the side benefit is that when you turn off the key, the headlights go OFF and anything tapped into the headlight circuit shuts off too .... so you won't have to remember to separately shut off the auxilliary lights and finding a dead battery the next morning. Lol, if you ever get them working again.
There's 4 female connectors that attach to the 4 relay prongs. Try wiggle them around to see if they're tight enough. Also, the cobra lightbars that I have (sealed beams) were grounded to the metal light shells. You might want to unscrew the rim and take a look inside at the connections. In my opinion, it's better to run dedicated ground wires back to the frame or battery neg. A caveat here though, when I ran ground wires from the auxiliary lights back to the frame, I had to snip the shell ground, otherwise the fuse kept tripping. For some odd reason, you can't have a double ground.