This technique will be foriegn at first and will take some getting used to. However, if you persevere and make this a part of your practice regimen, you'll be doing this on a gig in no time. Any pattern or rhythm you can play leading with your right hand, you can play leading with your left. As you transpose rhythms, you'll notice that you are forced to think about what you're actually playing, rather than just playing by rote. This can't help but improve your mental facility.
Some exercises follow.
Some examples of ambidexterity. Practice them slowly, building speed as you become comfortable. Here is a funk rhythm. Notice the grace note in the second measure. Play the two eighth notes at the end of each measure with slightly less force than the main backbeat on 3, but not light enough for a grace note.