would an 05-06 kawisaki have a 4 coil ignition system or a 2 coil ignition? does that refer to the amount of cylinders? I assume its 4 coil, for 4 cylinders. someone please confirm. thank you.

Older 98 and prior, engines (f2's f3's) had 2 coils with conventional style plug wires that managed the 4 cylinders.
Japanese 600/636 engines since about 99 have 4 individual coil packs that go right on each spark plug, no more high voltage coil wires to fool with like the old days.

Hope that explains it