I'm wondering if it's meant as a play on "trout tickling," which is basically an old-fashioned method of hand-fishing by stroking the trout's underbelly (how they got them to keep still for the initial "tickle" I have no idea) until they essentially become hypnotized and can then be snatched up out of the water. It was more a sport for poachers and poor folks than the country gentleman, but apparently quite popular in rural areas around the Depression. So the article might have basically been about methods for luring girls to your country gentlepad for some country gentling.
Squire Colin