What determines item box spawning at the end of the first Act on each level in Sonic 3 & Knuckles?

At the end of Act 1 of most levels, after you defeat the miniboss, the signpost falls out of the sky like so:

You can bounce the sign around for some extra points, which is great. But sometimes when it hits the ground, an Item box will pop up, allowing you to grab some extra rings, an extra life or a shield powerup (for the next Act).

But what determines when the item boxes appear? Is it random? Or is the chance affected by other things? For example,

• Do only certain levels give item boxes?
• Does bouncing the signpost around a few times affect the outcome?

According to this wiki, they are in static places at the end of each level.

In Sonic the Hedgehog 3 and Sonic & Knuckles, the signpost appears after defeating the first act's sub-boss, twirling as it falls from the sky. Jumping into the sign causes it to bounce back up into the air, adding 100 points to the score with each jump. If it happens to fall on the ground on one of three specific spots, it will cause a secret item box to appear, also causing the sign to bounce back up into the air. When it finally lands on solid ground, the face of the character being played will appear. Also, while it is possible to catch a glimpse of Dr. Eggman on the sign during this process, it is impossible to have the sign land on his visage.

This forum post seems to agree. It also claims that not only are the locations static, but the items are as well.