The part that involves the tuning spring is at neither of the locations mentioned- it is in the crankcase behind the water pump (driven on the same shaft). Since the pump is in it's own "capsule" in the clutch-side case, the case can be removed without draining coolant or molesting the pump/ seals in any way.

The KIPS valve is actually quite simple in it's operation (though it involves the coordination of many parts):

It all starts at the crank (more or less)- there is a spring tensioned centrifugal governor (or a centrifugal clutch if you will) that is put into motion by the spinning shaft upon which it is mounted (in this case the water pump shaft), dependent on RPM. At low RPM, the governor is disengaged and thus so is the power valve (which means it is operationally closed).

As the RPM climb, the governor "bites" (very similar to engagement of any clutch) and this drives the shaft which extends from the crankcase to the primary pinion of the KIPS valve on the RH side of the cylinder (under the plastic cover), pulling it out as the valves open. This pin has gear teeth and as it is pulled out, it actuates the network of gears/ valves to open. Now, this is all from memory so I may SLIGHTLY wrong on a few of the finer points...

As I recall there are three main valves- one in the central exhaust port which rolls clockwise or counterclockwise to open the exhaust port to "full round" (it is semi-round when closed). The other two are in secondary exhaust ports and rotate on a vertical axis to open these ports (I believe they are fully "shut" when valves are closed).

The cover on the LH side of the cylinder in the resonating chamber (and yes, as Tominator pointed out, you can spray carb cleaner in there to loosen "sticky" KIPS gears- though this is only a "timebuyer"- you still should dissamble and clean all the gears, rods, and valves a couple of times a year.). It's not unusual for gears and rods to break under the pressure of being bound in place by gook.

The little cover on the front of the cylinder (above the pipe spigot) is actually a bushing that holds the central valve/ gear in place.

The KIPS valve is perhaps one of the most overlooked items in Kawi maintenance, especially in the KDX models. The downside to this is there are probably THOUSANDS of people out there riding with valves that don't work properly and probably don't know the difference they are missing. KIPS valve operation is KEY to performance, moreso than just about anything else on these bikes.