Always ON. Protection for yourself and others. Far easier to see a vehicle with its lights on than without. Motorcycles have been doing this for years.
I am getting about the same values for voltage with my monitor. Original stock battery. Holding off on a Diehard H5 AGM battery until after the next update.
Use some 2x6 wood blocks or larger under the jack. Two if necessary. I bought a electric 12 volt jack and impact driver to use in changing wheels. Works well.