The obvious solution was to replace the petcock. It's a Mikuni part -- one of the few components on the bike not proprietary to Triumph -- that costs over $120 to replace. Since that's 120 times what I paid for the bike, you can imagine I wasn't too eager to do that. Instead, I jerry-rigged a fuel pickup using the original petcock, but every time I was forced to go to the reserve setting, it gagged on rust particles. And there's a limit to what you can expect from a $1.99 inline fuel filter, which was my Plan B.
So, I finally bought a used petcock on eBay, that only cost me 35 times what I paid for the bike. Since the carbs have been taken apart too often, I also had to replace a few screws.
Once I had wrestled the carbs back into place and confirmed that the replacement petcock actually did seem to work, it was time to take the bike for a test ride. So I put The Chick on the back of it, and we headed over to the gym. I stopped on the way to fill the fuel tank and when I attempted to restart the bike it made a 'sparking' sound beneath the seat and all the idiot lights went dark. I checked the fuses, which are pretty accessible; they were all good. Removing the seat to get access to the battery is an incredible fuss on that bike, but on an impulse I reached through to just shift the battery ever so slightly in the battery box.
That caused the lights to come back on, although it still just made a 'solenoid' sound when I tried to engage the starter. Embarrassingly, I had to ask The Chick to push me, but it bumped to life and I returned home to learn that when I was drawing a lot of power from the battery to run the starter motor, it was shorting -- from one or even both battery leads -- to the frame.
I insulated the frame rails near the battery with strips of bicycle inner tube. While I was at it, I rigged a better system for securing the Triumph's seat, so I'd have easier access to the battery in the future. Remind me to take my friend Tim Prentice to task, or at least as him if burying the allen bolts that hold the seat on w-a-y far in under the edge of the seat was a design decision he made. Who thinks it's a good idea to spec a seat that requires tools for removal? And as for running the battery leads right along the frame rails; wouldn't a little additional insulation have been a good idea?
Making this thing reliable has been like training a persian cat to hunt for truffles. If I'm lucky though, that's all the Triumph needs to be a decent commuter. It won't be a really safe commuter, since it doesn't have mirrors. (Incredibly, mirrors aren't required on a street bike in Missouri.)
But, it should be decent. That's good, because I now have an actual job, working at [NAME OF EMPLOYER REDACTED]. Look out, motorcycle journalism...