Though an elephant is not a ruminant, it produces an enormous volume of methane - 2,000 litres per day. Its effect on climate is insignificant because of small populations. I wonder though about the mammoth herds, if their fluctuating numbers played any feedback with northern hemisphere climate.
A confounding variable would be deforestation by mammoths, to maintain a plains habitat as elephants do for parts of Africa.
I can't puzzle this one out.