I was missing the Tzdata — tzdata v1.1.4 piece. Followed the directions to setup tzdata. Although when Timex is installed, it does install the tzdata dependency, but setting up tzdata requires more effort. Even with installing tzdata and performing the setup, I was not able to get the Ambiguous response with Timex but was able to with DateTime.new():

  def test do
    ts = timestamp(~D[2023-03-12], ~T[01:30:00], "US/Mountain")
    IO.inspect(ts, label: "test a valid time")
    ts = timestamp(~D[2023-03-12], ~T[02:30:00], "US/Mountain")
    IO.inspect(ts, label: "test a time that should not exist")
    ts = timestamp(~D[2023-11-05], ~T[01:30:00], "US/Mountain")
    IO.inspect(ts, label: "test a time that is ambiguous")
  end

  def timestamp(date, time, time_zone) do
    case DateTime.new(date, time, time_zone) do
      {:ok, timestamp} -> timestamp
      {:gap, timestamp1, timestamp2} -> # spring ahead, time in hour gap
        timestamp(date, Time.add(time, 3600, :second), time_zone)
      {:ambiguous, timestamp1, timestamp2} -> # fall back; which 1:30?
        timestamp1
      timestamp -> timestamp
    end
  end

Thanks for all the help and quick response!