Hi, Aimee! I’d recommend asking your teacher about this (and I’d also like to know what he says).
I don’t really see how that advice applies to second/third beats - at least the “step out with nothing in your head” part. And, at the risk of putting words in your teacher’s mouth, I think he might have meant that advice for the non-initiating performer.
(My two cents, I could be wrong. I just don’t see how you can effectively initiate a scene without any idea… and if so, then why are you doing an opening, or even asking for a suggestion?)
Anyway, second beats are a playing/exploring/heightening of an idea established in the first beat. That’s the big thing to me - you take the distilled form of the idea and take it wherever you want, however you want. All the other preconceived notions can be washed away (unless you like them and wanna use them).
So, yes, I think you have to initiate with some starting idea to make that happen. Without a thread to the previous beat, I don’t see how it’s a second beat of a Harold; it’d just lead to brand-new, non-connected scenes.