In and out of the cave under the seabed

Behind the broken gate, a shaft leads down to a small deep cave, but a platform keeps rising up it, and once in the cave there seems to be no way back up.
Nudge 1Where to look
The platform rises slowly from the bottom of the shaft to the top, pauses, and starts again from the bottom. It's a lift, of sorts.
Nudge 2A stronger push
To go down, slip into the shaft beneath it while it's on its way up. To come up, ride it.
What you needOther problems to solve first
Solve these first (each opens its own page, no answers on the way):
Show the solutionThe whole answer, with a video
Down: stand on the ledge left of the shaft; when the platform has just set off upwards from the bottom and passed above the ledge, walk right into the shaft beneath it and let Dizzy sink into the cave. Take the stars and the large gold coin. Up: swim up out of the cave to the ledge beside the shaft, wait for the platform to come up from the bottom, step onto it and ride it to the top of the shaft.
Why it works
The platform only moves while Dizzy is in the area above the cave, rising half a pixel a frame and dropping back to the bottom after a short stop at the top.