Another way to have rhythm in you left hand accompaniment is to hold either the little finger (LH5) or thumb (LH1) d0wn and 'flap' the other.
Watch this demonstration video.
That first version holds the little finger (LH5) down and taps the thumb 'off the beat'.
Here's 'the other way round' - thumb held and little finger tapping.
This doesn't feel quite as natural. (It's not!)
Rotation in the wrist is a crucial component in piano technique. Here's a version that focuses on rotation by alternating the left hand bottom-top, top-bottom (5-1 1-5).
Go on to the next 'Flapping Fifths' page for some more challenges to work on.
The Beat & Rhythm Workbook