Hunter keeps gagging- vet or wait it out?

My cat Hunter has been gagging for the last 2 days, like he's trying to get rid of a hairball. He's a short hair and doesn't get hairballs often, but he has before. I've only noticed him gag/hack three times, and this time some slime dribbled out of his mouth.

We haven't switched cat foods, but we have dialed back on dry food and primarily feed wet food twice a day with a small bowl of dry food left out for them to nibble on throughout the day. The only major change is we swapped out cats with my parents-- Louie wasn't doing well here and my mom wasn't able to handle a kitten. It's a long story but we didn't just swap cats out willy nilly just so everyone knows. It's been about a month and they're getting along well, despite the kitten being a kitten and irritating Hunter any chance she gets lol.

This cat, just like Louie, is a big eater, and so every time we feed them Hunter eats a few bites then walks away and the kitten takes over. We started putting Hunters food up and giving it to him later after the kitten falls asleep. He doesn't really seem interested, but I don't know if he just doesn't like the wet brand (still trying to figure out which he likes and doesn't- vet advised we go mostly wet food because he's overweight, and has had 2 episodes of that thing where he can't pee, I forget the name, but no crystals were ever found so he just got meds and has been fine), or if maybe he's sick or stressed out over the new kitten? Maybe he ate something he shouldn't have? (not sure what it could be, we don't really have much or keep much out)

Anyway, back to the point...

I don't want to wait too long if it's something like a hairball he can't pass, but he's not ACTING unusual at all (he doesn't eat a lot in one sitting so him not eating much lately doesn't seem that unusual). Just the wet heaving/gagging. His eyes also kinda close and he looks like he might sneeze.

I'm going to call the vet once they open and ask for some advice and I should bring him in, but wanted to post here too just to get some advice/opinions.

My boy did gagged about 3 times in 7 months. Seems like what you said about clearing hairball. He's a Shorthair cat and I brush him every morning. So I don't think it's hairball that's bothering him but it might be as we never know.
So I brought him to the vet together with the video I shot of him while gagging. The vet says that he's trying to clear his throat and it's pretty ok. And till now, never seen him gagging at all.
Best is shoot a video and show it to the vet. It's better than describing the situation. And heatvwhat the vet has to say about it.

I'm trying to catch a video but he doesn't do it often at all. In fact I've only seen him do it three times in two days. And it's over so quickly. Hopefully I can get a video. The vet said they'd call back and give me some advice since I really don't have the money to bring him in for just anything...so that's nice.

Yea, it's not easy to catch on video as we are not all the time camera ready and sometimes this happen over so fast and by the time you get your phone and turn on the video mode, it's all over.
I only caught it on video at his third time gagging.
I always take photos or videos of such abnormalities so that I can show it to the vet.
Just observe Hunter for the next few days. If he's eating normally, peeing and pooing normally and no gagging, then I think you don't have to worry that much but I'm not ruling out any other sickness as I'm not an expert. I'm sharing based on my experience with my boy.