Yes I can explain this and it's a very obscure aspect of the bike's wiring system. Here's how the Hall Effect Sensor can affect starter function. I'll try to do this by memory, as my notes on this work are back at the shop, so I won't include wiring colors for now.
Consider the starter relay. Like all relays, it has two "sides". Some people call them master and slave, others call them control side and controlled (past tense) side. The controlled side takes the high amperage input current from the battery and sends it to the starter whenever the relay is activated. The control side activates the relay. It's this circuit, the starter relay control side, that we need to consider.
The control side needs a power source and a ground. When the ground side is connected to a good ground, and the power side is "hot", the relay will click on and send power thru the controlled side to the starter.
OK so far? Let's continue. The control side power source is the starter button. When the key is on and you hit the starter button, electricity flows to the power side of the starter. But the relay still won't activate unless the ground connection is also good. Here's where the problem comes in.
You'd think the ground side of the relay would be wired directly to a chassis ground, as it is on many machines, but this is not the case on the K100. In fact the ground is provided thru the ignition brain and on thru the HES!!!! That's why an intermittent HES problem causes on-off-on-off starter operation with the starter button held down.
You can easily prove this point to yourself, but only if the bike will conveniently stay "dead" long enuf for you to conduct this test. Intermittent problems are always a pain to diagnose and work on cause they always seem to spring back to life just when you're closing in on them. Anyway, here's what you do. Identify the starter relay control side ground wire. Splice a new wire into it and run it directly to a chassis ground. The intermittent starter operation will now disappear! Of course, the bike will still cut out on you from time to time because the HES still has a problem. It just won't affect the starter circuit anymore.
When I figured all this out I was initially baffled by the seemingly unconnected symptoms: The bike would cutout and the starter function would get weird. Then it would all go back to normal. My attempts to solve the problem were hampered by the bike returning to normal. Ya can't fix it if it ain't broke. I got lucky, if a dead bike can be called lucky. The bike died on me and stayed dead. I had to call my wife to come get me in the pickup truck, but when I got the bike back to the shop, and it continued to play dead, I was able to discover the lack of ground at the starter relay control circuit. This breakthrough ultimately led to my diagnosis of the problem.
If this information can help you, half a world away, I will really be happy. It was a very satisfying mental challenge working this all out for myself, and the problem is so obscure, that it's not been published elsewhere. Aren't the Internet and this list great?