The deeper water table may be less influenced by rainfall and more by underground movement through submerged passage - I guess it depends what sort of rock you're in? Main Rising, Bathing Pool and Whirlpool in the Speedwell system in Castleton all fluctuate dramatically with respect to each other, and not always in periods of rainfall.
I was in there last week, and the water-level in the main streamway dropped by a foot in a few hours - there's a lot of pulsing inherent in the system, so it may have been the earlier depth was 'high' and it was settling back. So your case may be caused (like Main Rising) by silt buildup that's eventually released, causing a pulse for a while, and then blocking again. It may be something as daft as an old plank or gate somewhere causing a temporary dam until it swings open, releasing the water - like a giant flopjack.
Deeper voids not directly connected to the flow would also act as overflow reservoirs, so outgoing water might then stop flowing for a while until they've filled up, to continue back along the original level.