I think it's worth remembering that according to Jay's stepfather, he was not one to walk any kinds of distance, and would need to be driven a few hundred yards to get a haircut.
I can quite imagine Jay waking up with a bit of Dutch courage and deciding to go for a hike up the mountain to get a picture/video of the view (likes and shares are irresistible to teenagers).
Being that he's far from being an experienced walker, it wouldn't surprise me at all if that initial Dutch courage quickly vanished after getting caught in the leg by a cactus while sliding down the hill. Cactus spines can be particularly nasty and cause pretty severe swelling. This would have quickly sobered Jay up and possibly put him I to panic mode, or even shock. Shock can be a killer, especially if he's dehydrated from a night of partying already.
As morbid as it is, I suspect that he called Brad in high spirits, probably excited about his excursion, then slipped and caught himself on a cactus whilst on the call, prompting him to tell Brad he'd call him back.
The cactus injury begins to swell or otherwise turn particularly nasty, prompting Jay to panic and call Lucy (who appears to have the most experience with the island out of the group).
Jay then passes out/falls somewhere on the mountainside, south of the path. JMO.