Been playing Earthbound a lot more recently and this play through I've had a lot more encounters with the Photographer (Fuzzy Pickles).
Is there ways to trigger him to appear/avoid him?
The photographer in Earthbound is triggered when you step into certain areas for the first time. I believe there's an actual trigger for entering/standing in a particular location or on certain game events (ie, killing a boss monster or talking to a person) that causes him to appear.
This means that your encounters with him are essentially scripted - you can't choose when to meet him, and you can't meet him in just any old location. Strategywiki has a comprehensive list of all the locations, if that's of interest.
The Earthbound Wikia article for the Photo-Man It's possible to avoid him through use of Psi Teleport alpha, which makes you run real fast to gain speed before you teleport. Running through the trigger locations apparently bypasses the check for the photographer.