I recently completed a 2K+ mile tour on my 1985 K100RS.  I consider myself to be lucky to have returned home under its own power.  Early on, I noticed an irritating drop in engine power from about 3,200 rpm to about 3,700 rpm. I believe it is due to a lean period in the fueling, as it is worse when the high altitude switch is engaged.  On the final day as I rode home on the interstate highway at about 80 mph, the engine began to stop, start, stop as if there was a intermittent failure in the ignition. I pulled to the shoulder and mulled over what to do.  When I attempted to start the bike again, it responded immediately as if nothing was amiss. That didn't last however.  For the next 300-400 miles the bike ran well one moment and threatened to stop then next.
On the road I checked the following: the primary coil wires, the fuses, the battery post connections, the connector to the computer under the seat, the TPS and the main ground connection, all to no avail. 
In the recent past I rebuilt the alternator, installed a new battery, changed the fuel filter, cleaned the starter and replaced the spark plugs. The fuel injectors were cleaned professionally about 20 K miles ago. The fuel pump was renewed at about the same mileage. The wiring connector for the fuel pump under the left front of the tank is snug and free of corrosion.
On the road during the course of the engine's misbehaving I noticed the instruments didn't go dark, so I assume the fault does not lay in the ignition switch.  I also noted the charge light at times glows faintly even though the voltmeter shows charging is normal.  The brake warning light also came on for no apparent reason while I was underway. It then went dark again.
Where to continue with the trouble shooting?  I've looked at what seemed to be obvious possible sources of the problem, and found no likely fault(s).

Did you check BOTH ground connections?  The one under the tank and the one above the left footpeg.  Goofy stuff like you are seeing is quite often ground related.

Don't just tighten them, but take the terminals off and polish them with a small wire brush or some wet or dry paper.  Get them nice and shiny and then put some dielectric grease on them before you put them together.

Also, I was having a similar problem on a trip last April and it was related to the ignition switch.  It is entirely possible for the engine to quit and still have the rest of the electrical stuff working.  It certainly wouldn't hurt to get into it and clean up the contacts.

There are 3 circuits that are switched by the ignition switch.
1. Headlight and instrumentation
2. Ignition
3. Running lights (parking and tail)

So I'd agree with .75. It's entirely possible that the ignition circuit switching has failed while the others remain in tact. Like many here I've experienced the same problem. At first it was just little engine hiccups which got bigger and more frequent. Then one night the whole shebang went out at 110kph on the h'way. Made it to the side of the road ok. Fortunately it was intermittant so I was able to get home. The next day the sw. got a good clean. The contacts get a coating from old dry grease which then hardens in the presense of arcing I think. This makes me think that there may be something at play with the batttery when its voltage drops and this in turn is affecting the voltage bias accross the charge indicator light

Another observation I made was that I too found the brake warning light came on occassionally. I put this down to the running lights circuit going intermitantly at the ignition switch. As this circuit also powers the BMU, I'm guessing that the unit was resetting itself... hence, the warning light would come on.

im having trouble identifiing whats causing my bike to sputter and stall stall after running perfectly for about 5 or 10 k.....then it has to sit for a while befor it will start and  behave the same way again......the fuel pump electrical connection looks good......im thinkin mabe a temp sencer /switch might be faulty....any help trouble shootting would be greatly apriecated.

Your problem sounds like a heat related failure of the Hall Effect Sensors on the front of the engine.

They set the spark timing, and like a lot of solid state stuff begin to fail when they get hot, and work again when they cool off.  One way to check is to see if you have spark when the engine has quit.  Then when the engine has cooled down, heat them with a hair dryer and see if the engine still won't run.

If you can get a can of freeze spray, you can shoot them when they don't work and see if they start working again without waiting for the engine to cool down.

There is also a very slight possibility that the problem is in a dirty ignition switch.  This causes the entire electrical system to shut down.  Usually it only takes a couple twists of the switch to get things running again.  If that is the problem, you need to disassemble the switch and clean the insides.  There are instruction in other threads on doing this.

Have you checked vent for the fuel cap?

Could be the HES failing but I'm thinking 5 or 10 klm is not very far for the engine to get hot enough.
Sounds to me like the engine is starving. Fuel cap, as Brad-man suggests, may have a faulty pressure release mechanism but I'd say there's a good chance the fuel filter is clogged and a common occurance especially if the fuel pump vibration damper is starting to disintegrate.

When you look inside the tank, can you see black bits sloshing around?

I will put my money on the hall sensors