When using a second floor shower, the faucet continues to leak water while the shower head water is flowing. Too, there's no access to the pipes inside the wall, or a cut-off valve. It's done this since the house was built in 2005. Any ideas to resolve this issue?

Assuming that you mean that while the shower is running there is water dripping out of the tub spout below?

If so, then there are several causes - can vary depending on how your fixture is set up to divert water from the lower tub spout to the upper shower head.

If you have to lift a tab or push up on the bottom of the tub spout, then the seal up inside is not making contact or is damaged. You can replace the seal (if you can find a match) or you can replace the entire spout as they are not that expensive.

If you turn a lever or pull a tab up near the faucet, then there is a washer inside that will need to be replaced. Here too, the tricky part if finding the right replacement part. Most home stores have an extensive selection of faucet parts but it's usually best to remove the damaged part from your faucet and take it with you to get a perfect match.

or, it might be a simple adjustment of the diverter valve that will allow the diverter to close the spigot opening