It looks like your tree is in the process of dying :-( I'm guessing some droughty summers and the mentioned neglect have contributed to a stressful situation that may have prompted a pretty serious disease issue. Taking in samples of the dead portions to your local cooperative extension service should be able to confirm that.

All you can do at this point is to remove the dead wood. Use pruning saw and pruners that are sterilized after each cut. Limit your pruning to just that - removal of dead wood. Japanese maples seldom need any routine pruning. And keep the tree properly watered this summer - they do not tolerate drying out well

I'd cut all the dead wood, and prune the live parts back hard! They say not to trim more than 1/3, but I'd go back to half, probably eliminating the entire left side and make it a single trunk tree.

If you baby it it will probably die, or look like hell. If you prune it hard, it will fight to survive, and start back budding like mad. You can then leave it alone for a few years and be able to prune it into a normal looking tree.

If it dies, oh well. It was probably going to die anyhow. Shrug it off and go to the nursery and get a new one.

Samples of dead portions can only be diagnosed as dead!

The preferred sample is a branch with both live and dead tissue on it. Plus an overall image.

That said, I agree with the first post. I suspect it's too late for the tree.
I also agree with the "remove only dead" advice. The tree needs all the photosynthesizing surface it can get.

I would cut out the dead and pay attention to watering.
Cutting back live wood by half would ruin the branching pattern.
Mike