How do you handle an elderly neighbor of a client that harasses you?

Sorry, this is reportable to the police. It is an assault. Go to the station and make a complaint. Has the neighbor any prior evidence of odd behavior? This person needs to be investigated.

I would find another agency to work for.

If he does this again, call 911 and report the assault.

Anyone that comes up and touches you is committing assault. You can call the police and file a complaint.
There is the possibility that this neighbor has dementia (one of the things that is lost are filters as to what is an acceptable norm )
Does this person live alone or is there someone else there? This might be something that you could discuss (outside the house) with another member of the household.
But I would not hesitate to call the police if this person accosts you again

My client is being placed in a nursing home on November 1st. A lawyer and social worker came to do paperwork for Medicare to pay for it. She is very upset because a funeral home is coming on Wednesday to plan her funeral. I do not ask questions about all of that. I know when she goes into the nursing home, the family wants to pay me to visit her a couple times a week until after the holidays.

I'm not sure what authority the agency has against a private citizen who isn't a client or or employee of theirs. You should report him to the cops, and they will probably refer him to social services if he seems cognitively impaired (which sounds like it). If the home is in an HOA, I would contact the president and discuss this -- this person may be willing to talk to him (but doubt it will do anything if he has dementia). Or, he might be willing to find contact info for his family to pass on the report of his behavior. Or, you could report him to APS as a vulnerable adult and get him on their radar. That should get someone's attention. IF it happens again, call the cops, video him, and still report it to your employer just for good measure.

Your agency should be proactive in contacting social services and law enforcement about this person's assaultative behavior.

The fact that they are not taking action tells you that they don't care about the welfare of their employees.

Ignore it? That’s odd advice. You did the right thing to report it.

I would tell him to stop immediately. No one would appreciate being smacked on the butt. It isn’t flattering or cute.

So sorry that you have dealt with his behavior.

I spoke with my client's daughter in law about it today because my client told her. The neighbor has mild dementia and was a judge and his son is a prosectuting attorney. She said the neighbor women are all complaining about the same thing. She apologized and said she would have her husband call his family.

Stop being nice to this old Fart! Ignore him, avoid him, growl at him, assume a Kung FU pose, alert his caregiver, whatever!!! I doubt it warrants a 911 call; don't they have enough to respond to without this?

I would also invest in a can of pepper spray, one that shoots a long distance. Don't hesitate to use it. Don't let him get near you.