When I did this quest, I found this fruit hard to forage. Eventually, I spent some time standing on jungle texture tiles and still did not find it.
On a hunch, I noticed that some of the jungle trees had bright purple on their leaves, where others did not. Thinking that they looked like ripe fruit, I stood directly next to the trunk on one of these purple fruited trees, and got the Kejekan Palm Fruit on the 1st forage!!!
A day later, doing the quest again, I thought perhaps it a fluke, so went to test it. Standing under another purple fruited tree, I foraged and got the Bamboo shoot. I waited, and forage again, and got the Palm Fruit!!
Hope that helps!
~Urgon