How does the secondary effect of Heat Metal work?

This question is a more straightforward combination of my two previous (hopefully soon to be closed) questions here and here.

heat metal states:

If a creature is holding or wearing the object and takes the damage from it, the creature must succeed on a Constitution saving throw or drop the object if it can. If it doesn’t drop the object, it has disadvantage on attack rolls and ability checks until the start of your next turn…

I am unsure how this disadvantage mechanic functions as a whole. When do you suffer from it and in what ways (if any) can you end it?

For example:
What happens if you fail the save but cannot drop the object? Does dropping the object later, on your own turn, do anything?
What happens if you succeed on the save? Does dropping the object later, on your turn, do anything?

I would like it to be assumed that you cannot willingly drop a weapon when it is not your own turn as shown in This Q/A; however, heat metal can still force you to drop the weapon.

I would also like it to be assumed that the saving throw is not optional as shown in This Q/A.