Leak from tub shower

After a couple of years of intermittent problems (and time-consuming repairs) I think I have determined where our tub-shower leaks - through the opening in the wall where the spout comes out. When somebody showers the water drips down the wall, hits the spout and enters the wall from there.

How should this be sealed around here? The current spout has no escutcheon plate and no grouting. The water fromn the shower just hits it and (I think) snakes its way into the wall and onto out newly repaired den ceiling. Any advive would be helpful. Thanks

Remove the spout. Depending on how big the clearance is around the pipe coming out of the wall, you should fill it with caulking or plumbers putty. Then put the spout on. You can try to seal the edge of the spout to the tile with caulk. It takes a little patience to get a neat job here, but it is worth the trouble.

leak

Given the way the spout is usually installed, that would be possible, but not usually the cause. But a simple bead of caulking where the spout touches the tile would be enough to eliminate that as the potential source.

leak

I would go to the access door and put a bright light there. Then splash water on the business side of the tub surround with a pan or glass and then look in the access. You may be surprised to find more than one leak.
Then you can determine if you need to putty, caulk or both.......