Well, I was right about the basic clutch adjustment being straightforward. But that doesn't mean I was able to figure it out on my own! Ha.
Even with the shop manual and the Haynes manual in front of me, I was pretty clueless on this one. Luckily the folks over at the TriumphRat forums were able to help me out. Check out this thread for a rather detailed explaination of the basic clutch adjustment. It's threatening to downpour right now but I'll take the bike out in a few days and see if the adjustment did the trick.
I'm starting to put together a document which captures the information I've come across on Triumphs so far, I'll host it and post a link here when it is further along.

After a bit of troubleshooting on the ignition path I determined the right-side condenser was bad, so I replaced it today. The right-side exhaust still expels cool air, but the bike doesn't die immediately when I pull the left plug. So I think the right cylinder is running, but perhaps not very well. A timing/valve adjustment may be in order.
This week's new issue is with the clutch. The bike always dies when I put it in 1st from neutral unless I have the throttle open a bit. Also it seems to require a couple of taps to get it into 1st, seeming to catch somewhere in the middle. Lastly, the other day it was creeping forward when I was trying to get it into 1st gear with the handlebar clutch lever fully engaged. I guess I'll try adjusting the tension on the clutch cable as that is fairly straightforward.
Ah, the joys of owning a vintage bike! Actually, it's not so bad. I enjoy troubleshooting the bike and I can still ride it around. My riding skills are improving, hopefully I'll feel confident enough to take Pearl out for a medium length trip before the riding season is over here in the NorthEast.

Houston, we have a problem. I'm pretty sure my bike is only running on one cylinder. Symptoms are cool air coming out the right side muffler, and if I pull the left side plug when the bike is running it dies immediately. Hopefully this isn't anything major and I can resolve the issue myself.
Since my last post I finally got the tank correctly mounted. I also did a bit more work towards getting the bike cleaned up, mostly spending a lot of time trying to get the spokes shining again. Soon I'll be fixing a few spots on the paint job that need attention. I'd also like to come up with something to cover the battery without resorting to the stock side panels. There may be a minor nagging issue with the electrical system. The other day I took the bike out for a spin at night and after about 15 minutes it died..it took about 5 minutes to get it started again. I have a strong suspicion the battery isn't holding a charge well and running with the lights pushed it over the end. Some tests last weekend seemed to confirm that (the battery won't hold more than a 12.3v or so charge, not terrible but not great; load testing the battery gives results in the lower end of the acceptable range). I may end up replacing the battery and praying it's not the alternator.