By switching from QWERTY->Dvorak->Colemak my keys had switched positions in each transition. I purchased a 'keyless' keyboard to avoid confusion if I happened to look at the keyboard. For example why did I just press "S" but type "R"? It would be very confusing for my brain.
When staying with a familiar layout - I would still recommend hiding the keys from sight as it forces you to internalize where the keys are rather than looking at them to find them. The idea behind touch typing is you know the distance between each character and can type it accordingly from memory instead of having to look for each key. :)
"I purchased a 'keyless' keyboard to avoid confusion if I happened to look at the keyboard. For example why did I just press "S" but type "R"? It would be very confusing for my brain."
That confusion is precisely the stick that keeps you from looking at your keyboard. If I glance down and get confused, that stops me looking down much faster then if I glance down and just don't learn anything. At least, that's the theory.
Note, just in case it wasn't clear, by "rearranging" I mean moving the labels and not moving what key location generates what input.