Ground water drainage problem

I live on the edge of town in a remote wooded area. My 40 year old home has two sump pumps. The one located in the crawlspace connects to the drain tile around the house foundation and discharges the water out via a drain line about 100 feet long. The other is just a hole intended to drain the half-basement, which is about 2 inches above the crawl space floor. The wash machine empties into it and the water is pumped out via a drain line about 100 feet long. The house is on high sloping ground but one home adjacent to mine is about 4 feet higher.
Initially the pumps never ran except for the basement one and only when discharging wash water. For several years now the pumps start to cycle about one day following a rain. The pump, which is located in the basement hole also, cycles. The drain line discharge is about 6 feet lower than the house foundation and is working. I can see no wet spots around the house. I have no idea where the water is coming from. The crawl space ground around the sump hole is damp
I have to assume that the water is coming up out of the ground, as it is the only way it could get into the basement sump hole. A subterranean stream perhaps? I'm stumped! Any suggestions would be appreciated.

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