Because implementing cron is always a good idea.

times.rb

require 'date'
require 'minitest/autorun'

class Time
  def self.normalize time
    dt = DateTime.parse(time).to_time.utc
    Time.utc(Time.now.year, nil, nil, dt.hour, dt.min)
  end

  def inbetween start_time, end_time
    if start_time < end_time
      (start_time..end_time).cover? self
    else
      start_time < self || self < end_time
    end
  end
end

describe :in_time do
  norm = ->(ex) { ex.map(&->(t) { Time.normalize t }) }

  describe "times that are in-between" do
    [
       ["T11:00:00-05:00", "T04:00:00+10:00", "T21:00:00-05:00"], # Mia's example
       ["T00:00:00-00:00", "T01:00:00-00:00", "T02:00:00-00:00"], # | S ? E
       ["T23:00:00-00:00", "T01:00:00-00:00", "T02:00:00-00:00"], # S | ? E
       ["T23:00:00-00:00", "T23:59:00-00:00", "T02:00:00-00:00"], # S ? | E
       ["T00:00:00-00:00", "T06:00:00-00:00", "T00:00:00-00:00"], # S ? E=|
    ].map(&norm).each do |start_time, check_time, end_time|
      it { assert check_time.inbetween start_time, end_time }
    end
  end

  describe "times that aren't inbetween" do
    [
       ["T00:00:00-00:00", "T01:00:00-00:00", "T02:00:00-00:00"], # | ? S E
       ["T23:00:00-00:00", "T01:00:00-00:00", "T02:00:00-00:00"], # ? | S E
       ["T22:00:00-00:00", "T23:00:00-00:00", "T02:00:00-00:00"], # ? S | E
    ].map(&norm).each do |check_time, start_time, end_time|
      it { refute check_time.inbetween start_time, end_time }
    end

    [
       ["T00:00:00-00:00", "T06:00:00-00:00", "T12:00:00-00:00"], # | S E ?
       ["T23:00:00-00:00", "T06:00:00-00:00", "T12:00:00-00:00"], # S | E ?
       ["T18:00:00-00:00", "T23:00:00-00:00", "T12:00:00-00:00"], # S E | ?
    ].map(&norm).each do |start_time, end_time, check_time|
      it { refute check_time.inbetween start_time, end_time }
    end
  end
end