It doesn't really matter. But there should be some mechanism. A rocket attached to your feet works quite well if you ignore the exhaust for purposes of reference.

If you want a useful thought experiment about physics then you need to give reasonable physics tools. Otherwise you get something like "Pretend you are an inanimate green blob. You can't climb a hill, can you? Therefore climbing a hill is an illusion."

If you have a rocket on your feet why do you need to drop something to figure out if you are accelerating? You can feel the pressure on your feet.

The only type of acceleration that is undetectable is gravity - and gravity will effect the dropped object exactly as much as you.

Great! You just simplified the experiment!

Dropping something was only one idea, but feeling pressure is much simpler.