Wife recently started having auditory hallucinations (music) at night. She suspects neighbors are doing it to her on purpose.

Ired, I would start with her PCP.

The thing you need to be worried about is a brain tumor. I have a 60 year old friend who had brain surgery yesterday to remove a massive and thankfully benign tumor that was causing all sorts of weird symptoms. Thankfully, neither he nor his wife wrote it off as nothing.

A good neurologist would be a good start. At the very least, she needs some imaging of her brain done.

"Honey, this thing with the music you hear? I'm concerned that it's something we need to investigate so we can make sure it's not physical. I've made an appointment to see Dr. T tomorrow"

Please let us know how this works out.

The internet is chock FULL of information for you. Look up auditory hallucinations and you will find all sorts of them including Charles Bonnet syndrome. Oliver Sacks was so fascinated with the way music affects elders and is remembered by them years after all else is lost that he wrote an entire book on the subject. I recommend it to you. It is called Musicophilia.
It is not uncommon for elders who don't know their own wives or families nor even their own name or history to know the words and tunes to many songs.

The next step for you? Evaluation by your wife's doctors; request a referral to a neuro-psyc specialist for baseline testing;

I wish you the very best of luck.

Good article:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5420178/

You get her tested for dementia/cognitive decline by speaking to her doctor about these auditory hallucinations she's having. She's also exhibiting paranoia by thinking the neighbors are playing music to purposely irritate her, and won't believe a silent tape recording. All classic dementia symptoms and not "normal aging memory deficiencies " at all.

That said, there is a condition known as Musical ear syndrome, or MES, that causes auditory hallucinations where patients hear music or singing that isn't there. The condition normally occurs in those already suffering from hearing loss and is a result of the brain ‘filling in the gaps’ caused by the hearing loss.

If your wife suffers from hearing loss, MES could be what's going on. But the condition does not cause paranoia.

Best of luck to you.