Your neighbor is an assaholic. Reminiscent of a neighbor I once had, which caused me to create that special word for him. Some people just are addicted to being an a$$.
My neighbor also had issue with me watering my garden when some water drops landed on his driveway. He complained to me, but I ignored him. I can understand if the water was hitting his car due to possible water stains, but that was not the issue as the water was grazing his town issued trash bins.
Anyway, he was so pissed off that I ignored him that he went and parked his golf cart on the public road where sprinkler water was overshooting. The next thing I know, the police were at my door because the neighbor claimed I turned on the sprinkler to get his golf cart seats wet. Well, the police were familiar with the assaholic next door due to years of complaints from everyone on our street. The cop was no dummy as he realized the area under the golf cart was wet, so it was obvious that the neighbor parked his golf cart there AFTER my sprinkler was turned on and tried to set me up. The police ended up giving him a ticket for not following the towns rules on Golf Cart usage. (he needed to have insurance on it and a head light and a six foot pole with a red flag). Poetic justice. You cannot fix stupid.
About your sprinkler....since your neighbor has some mental issues, this situation can escalate and trust me, he can make your life miserable, he can and he will. I would get one of those hoses that are a soaker hoses. It is a hose that you wind in and around your garden. The hose has a bunch of holes in it and when water goes through it, the water leaches out into the ground. That will not "water" his fence. I know, I know, you should not even HAVE to buy a soaker hose, but to keep the peace, it may be a good investment. Sure, you could jump through hoops and please him for manipulating you, but install the soaker hose when he is not home. He will wonder how on earth your garden is flourishing. Also, a soaker hose is a huge saver on water consumption as well. Put the hose down, cover it with mulch to increase water retention and watch him scratch his head. LOL
Remember, you cannot fix stupid and in the interest of living next to an assaholic in as much peace as possible, sometimes you have to reason with unreasonable and come up with creative solutions for "ridiculous problems".
You would not believe the bullsheet I put up with at the hands of my neighbor, his wife and his teenage kids. I could honestly write a very captivating book on the subject. My advise to you is to imagine your body is coated with wax, so whatever that idiot next door does or says will bead up on you and fall to the ground, like water on a freshly waxed car. Ignore the ignorant.
I will say that once I put up surveillance cameras, the assaholic backed down because, well, because he is a cowardly bully.
EDIT: Oh, I forgot about something the assaholic did. After he received his ticket for not having his Golf Cart "road worthy", he set his automatic sprinkler to go on at 1am to shoot water 15 feet into our back yard over my seating that had cushions on them, saturating my cushions. I only realized this when I happen to wake up to use the bathroom when I heard his sprinklers. So, since I am a night owl, I removed the cushions before I went to bed. My son woke up very early for work, so he put the cushions back before he left for work. Now, mind you, in the mean while, all that water was watering my lawn and it was looking pretty good; at the water consumption costs of my assaholic neighbor. Assaholicism personified! Ha!! He is such an idiot that it took him about three weeks to realize I outsmarted him. Well, I have to admit, I reported his sprinkler usage because we had water bans on weekends that prevented lawn watering. He got another summons for that!! Like I said, you cannot fix stupid. Like he thought I would not also record that activity on my surveillance cameras. He was so easy to outsmart!!