Yeah, not an ideal place to have a spring. You could try cramming a pipe in the hole and see where the water rises to. That will let you know the water level would be before not acting as an inlet any more.

If I were to guess, the spring is related to the small dry creek bed above. It may be an old buried creek bed of gravel the water runs through, so it may have to back up quite a way to reach your full pool, and by then water may be finding a new route somewhere else.

I would do as you are suggesting: Dig a trench just above the water line in hopes of intercepting the flow of water and dam it off with clay, liner, or both. Hopefully the water from the spring will back up, and eventually water will overflow your plug above the full pool line. The risk is not finding the spring where you expect.

Can you hand shovel some of the spring to get an idea of direction of flow?