Thanks for your replies, @
Triple Jim and @
ducatiman! I appreciate y'all's help
I didn't notice black smoke from the exhaust pipe, but I also wasn't observing it too close, and it was at night when it last fired up. I did smell a little bit of burning and thought I saw some smoking at first, so it's very possible.
In taking a look at the carbs, externally, they didn't look horrible. I trust Ducatiman's work, so my guess is there's probably something going on outside of the carbs (especially since this happened before and occurred immediately as I fired the bike up). We're working together to double-check the petcock and the carbs.
I looked at the tank, and it looked good. I have a clear fuel line and removed some gas from the tank, and there is minimal rust; there might be some flash rust, but I only saw one or two specks.
Seems like a valve adjustment is the next step. The bike's at 10,118 miles. I doubt it's had a valve adjustment seeing how the previous owners maintained it (ex: the tires are 10 years old, which is what I have to change once I get it running).
Will do on checking the battery.
Thoughts on checking the airbox? Could a dirty filter be causing this issue?