I assume that some increase in the blink rate is normal being this is a generator as opposed to an alternator or alternator, the differences of which my father taught me.
Sorry, I can't agree.
First, regardless of either a generator or an alternator, because the system relies on a battery, the system voltage has to be DC.
A generator produces an AC output that has to have an external rectifier to convert the AC output to DC.
An alternator is a generator with an internal rectifier so the output of the alternator has already been converted to DC output.
Unfortunately, Kawasaki calls the "Black Box" a Voltage Regulator when in fact it is a rectifier / regulator. Inside the "regulator" are 3 silicone diodes, one for each phase that allow the positive half of the AC wave to travel to the positive cable and 3 silicone diodes that allow the negative half of the AC wave to travel to ground. The difference in voltage between the positive output cable and ground is monitored and regulated to a set output voltage. In the case of the regulators supplied in our bikes, the regulator is a shunt type regulator. Any excess voltage above the set point is shunted to ground which in effect is "shorted" to ground. So the stock regulator causes the generator to be putting out full output 100% of the time.
A more recent update to the charging circuit is to install a series type rectifier / regulator. In this update, there are still 6 silicone diodes to rectify the generator output from AC to DC voltage. The regulator portion instead of shorting excess voltage to ground, instead opens the circuit of the positive side and closes the output side and regulates the output by "turning off / on the circuit. This in effect reduces the load on the generator when the system voltage requirements are low/ It's estimated that for most motorcycles this could reduce the load on the generator by between 20 - 30 %.
The battery in the circuit acts like an accumulator in the system and buffers the output of the charging circuit and helps to control the system voltage and gives a more softer feedback to the regulator of the system voltage thus allowing the regulator a better chance to control the voltage at set point.
You mentioned that one side flashes faster than the other. the side that flashes faster has a higher resistance in that circuit than the one that flashes slower. Resistance can be due to corroded connectors or corroded switch contacts, or even a difference in light bulbs installed. I've come across the light bulb problem a few times. Guy comes into the shop and says he just replaced a turn signal bulb and now the turn signal either flashes faster or slower than the other side. a 10 watt bulb put in place of a 20 watt bulb will completely screw up the flasher.
You also mention that the flasher changes speed depending upon the motor rpm. This tells me that the system voltage is different at different rpms and the battery is suppose to buffer that issue. When the system current requirements are high, the battery is supposed to make up the difference between the charging voltage and the demand until such times as when the demand is less than the charging output amperage, then the charging circuit is supposed to "fill up " the battery.
Bottom line- you're not done with this issue. Lots of things to check
I hope some of this info helps.
KB