I know that the US skipped islands during their fight against the Japanese in order to save time, resources, manpower, etc. But did they really just leave every other island they didn't invade alone? What if there was a ton of Japanese on that island that somehow managed to stage some kind of counterattack or sabotage? Or did they just avoid occupation?
Islands skipped during the Island Hopping campaign were left to "wither on the vine," such as it was.
If an island wasn't required for the advance, it would be neutralized. Sometimes that meant a series of bombing raids to eliminate whatever aircraft were stationed there, sometimes it meant just ignoring it altogether.
Once the US Navy came through an area, the Japanese were usually unable to support the skipped islands altogether. Rabaul, for example, was reduced to being able to (barely) defend itself, and not do much else other than feed itself, despite having nearly 70000 troops there at the end of the war. That's a substantial force, but they could be safely ignored because its reach was roughly that of a rifle.
Smaller islands would be brought to the brink of starvation, or even farther.
As far as counter-attacks went, there was no real threat of that. Using Rabaul as an example, with no aircraft and no shipping the Japanese troops couldn't leave the island of New Britain. There was little else on the island worth owning, and while there was an American base at the opposite end, it was nearly 300 miles away over some ridiculously rough terrain.
Basically it came down to mere survival for the skipped islands. They might still get bombed or shelled, but they often were more interested in obtaining food. That usually precluded any attempt at counterattack.