Is this thing here a helper or a model, or something else?

These methods are not generating any HTML, so they should not be in a
view helper. Like you said, they are not needed for controller function,
so they shouldn't be in the ApplicationController. So I would put them
in your model.

You can put this logic in a module in your lib/ directory. This way if
you need the code in different models, then you can just require/include

module ChunkyTime

  def set_start_time ...
  def set_end_time ...
  def get_time_blocks ...


class MyModel
  include ChunkyTime