These Suzuki's have the main line from the fuse panel leading out to a junction box that splits power to the components.Lights,fuel pump,ignition and such.
This wire from the fuse panel will lose contact with the junction box intermittently causing a whole host of things to go wrong.
If you think this bit of insight came easy you'll be sadly mistaken .
If your Suzuki acts funny try this.
Actually, on the TL (the R, and I think the S also), the battery lead first goes into the starter relay. The main fuse is a part of the relay assembly, and behind that it splits it out to the ignition feed and the main feed, which then go off and feed everything else in due course. The connection to the starter relay is done through a cheesy cheap plug that's well known for corroding and failing; since that carries the entire system, the result is usually a dead bike, or at least some really funny problems. Many of the TL guys either (a) bypass the headlights and the R/R around that to cut the current down dramatically, or (b) solder the harness directly to the relay.
I actually had this connection get weak on me once; the result was a bike that ran fine at speed (though the tach would drop to 0 and stay there) but stalled instantly when it got close to idle, and wouldn't restart (no juice to the ignition, if I remember); whacking the connector a couple of times usually solved the problem enough to get home.
I don't think there's a junction box, exactly, in the TL's harness, but there are plenty of multi-pin connectors and they're also known to corrode. My headlights kept going out a while back because of this. I had been thinking of buying some big mil-spec Amphenols to fix that, but the thought of installing 20 lbs. of connector wasn't appealing.
In addition to what Gus said,
Could be one of the SCR's although they usually fail in the ON mode. That would cause a crowbar at some point. It could also be a rectifier that has some breakover problem, where when the reverse voltage rises to some high level, it lets it through (backwards).
Either way, replace the Rectifier/regulator unit and you should be OK. However, check the stator before installing the new regulator unit. Bad Rectifiers have been known to fry stators.
Did you check charging CURRENT?
The times I've checked the stator before, it's usually given me about 75 VAC across all poles, which is in spec. This time, I just ohmed it out; it was about 0.5Ω between any poles, and no continuity to frame, which is correct. I did get about 75 MΩ to frame when I used that setting, which then kept rising through around 140 MΩ, but I'm taking that as a good insulation reading. It's possible that it could have a turn-to-turn short that wouldn't show up on that test, but at the moment I've got no reason to think the stator is bad: up until the regulator dumps, the voltage comes up very quickly with rpms, and even after that I didn't see any irregularity or imbalance between phases on the scope. If it is going bad, it seems like it is being awfully organized about it.
I did not check the charging current, since my Fluke clone doesn't have a setting over 10A and I don't feel like risking it when the voltage pretty well speaks for itself. For what it's worth, the first time I checked, the battery was well discharged (about 12.2 V) and the charging voltage never got much above 12.5 V at 5000 rpm. That's not a valid result according to the manual, since the battery was so low, but it still makes me think that the R/R is malfunctioning: even in that case, it should be working to pull the bus voltage up over 13 V or so, I would think.