As someone who's actually had this problem (in an urban area) and actually solved it, here's what I did: Changed the shape of my fence so the amount of privacy the serial shitter was afforded was significantly reduced. Changed the position of my gate so that it no longer opened near the convex corner the shitter favored. They found a better spot and moved on.

You think someone is shitting outside in a public space and your plan is to surprise them in the act?

Form the annals of what could possibly go wrong.

I don’t know where you live, but I am going to assume it is suburban or rural, is it possible to light the area?

Raccoons like to poop on top of their old dried poop. raccoon poop looks a lot like human poop. especially when more than one animal is using that latrine.

in the forest they often do it where two trails meet.

think about that before jumping out of a bush.

and if it was a raccoon don't handle that poop please. call animal control.

[edit to add] if you want some nightmares; google 'pinworm human infection' and then stay far away from raccoon droppings.

Jump out of the bushes while furiously masturbating. Scream at them to "KEEP GOING I AM ALMOST THERE PINCH OFF THAT HAWT STEAMING LOAF DADDY". Pretty sure one of two things will happen: Either they freak out, pull up, and high tail it out of there never to be seen again, or they lock eyes with you and maintain that connection through a slight squint and some grunts. Make sure you record it and post this to the internet.

Can you install a trail cam ?

Or just poop in that spot to show dominance!

take a bigger shit on their shit. assert your dominance.

Follow them home and shit in front of their house

In 2 days time on Ask Lemmy:

There's some creep hiding in bushes in a path which is connected to the gates of my neighbours house. What do I do??

What's the maximum amount of time you could tolerate hiding in the bushes with spiders & bugs, unsure when/if the serial shitter might ever return? Would you be willing to hunker down in the spider bug cold pokey bushes all night long & all the next day, and on day 3 at 4:42am you finally catch the shitter in the act? Will you have no tent? No sleeping bag? Snacks? Activities to pass time? Do you not have a job & duties to attend to, this wouldn't interrupt your week at all? Probably much easier to install a camouflaged motion-sensitive camera to capture the shitter. Then what you do? Turn the camera footage into the police.

Motion activated sprinkler. Works if it's human or animal, something like The first result on Amazon, just an example not an endorsement off the particular product

Could be a fox? 🦊

Buy a camera. Catch them in the act. Call police. Have them arrested. Sadly this is the only way to deal with people (assuming it's a human doing it).

Trail cameras can be quite inexpensive

Sounds like a territorial claim. You should probably do a bigger poop next to theirs in order to assert dominance.

Push them backwards into the shit. What you do to them when they are laying on the ground is up to you.

How rural is your path? I discovered recently that big fat raccoon poops are very similar to human poops.

Can You Go to Jail for Pooping in Public? https://legalclarity.org/can-you-go-to-jail-for-pooping-in-public/

It's possible for legal consequences if you can get video of them doing it.

Some sort remote controlled spring trap to fling the poop up onto their butt.

You observe the poop is literally black, and your conclusion is it must be from a human?

set up a few video cameras to catch them. Then once you know who it is, send stills and videos to their family. post on social media.

Hide out and spray 'em with the water hose or a supersoaker.

Only bad thing is then you have wet human shit in the same spot.

You could buy a toy camera. Pretty sure most people don't want to shit in front of a camera

Super soaker full of pepper spray/oil. Spray them in the any sensitive exposed area.

Like everyone else has said, put some cameras out to confirm it’s a human (it’s probably not). If it is a human you may recognise them, and if it’s a cat or something there’s probably some kind of deterrent you can buy.

Bear in mind local laws. Where I live filming people on the public street is a grey area legally, using a hidden camera to do it would probably be considered illegal. Not saying don’t do it, just don’t try and submit it to the police. If it’s a person tell the police you saw them doing it from the window or whatever.

Do you live in an area with lots of homeless? That seems most likely who would do that. Or some mentally deranged person. Either way, be careful with those types of people.

You could try the photography/videography aspect to bring them to justice or the classic scare and/or beat them with a baseball bat

Find out where the shitter lives and return the favor.

I've decided I'm gonna hide in some bushes nearby and catch them doing the deed. But what do I do then?

Back in the good old wild West lawless days I'd say it'd be a great opportunity for vigilante target practice, culling the miscreants from our population. But that's probably illegal nowadays.