The entrace to Wayward Cave that has Gible in it is hidden under the Cycling Bridge (aka Route 206). There is a more obvious entrance to the area to the east of the Cycling Road, but it does not have Gible in it. You can only find Gible in the hidden part of the Wayward Cave.
It can be quite hard to find the entrance; however, I found it relatively easily by just walking into the walls and looking for an entrance, continuing to the next wall if I couldn't find it.
You'll know if its the correct cave if you see multiple Strength rock puzzles and slopes that you require a Bicycle to cross.