Ambidextrous Pitcher Question

Originally Posted by UMP25

For the first time in my career, I had this last year in a CICL game. I noticed the pitcher using a different hand when a lefty came up to bat following a righty. At first I thought I was imagining things--not an impossibility--then the next batter was a righty again and lo and behold, the pitcher goes back to the other hand to throw.

Question for you - where did the keep their other glove when pitching - behind the mound or did they just put the same glove on the other hand? Just curious.