Others have pointed out the correct start point but not linked it to a method.
I call it Coupling
After @justhalf's comment and further review I see that my method is just an extension of pointing pairs, which was already employed on the puzzle. So I'll update the rest of the answer from here to explain what I did in addition. For those unaware of what "pointing pairs" are (like I was, even though I used the method) here's a link to information on that.
Using pointing pairs:
you find couples of pointing pairs that are linked together in a set of 4, which regardless of which number is placed in it can also eliminate candidates.
I was able to do that in this image:
You can see here, regardless of whether you put 4 or an 8 in r2c1, r3c5 will be the other, which means (without guessing) you know r3c3 cannot be a 4.
I don't have any other name for it, but the way I see it
these 4 positions are coupled together, forcing an additional elimination.
Using this as a starting point, I was able to logically fill out the rest of the puzzle:
Please excuse my poor writing. I think you can get the gist. I did this with one hand on my phone because my 5-month-old refuses to not be held and walked around the house. Lol
This is not a "fix-all" method. There are puzzles at the highest difficulty that cannot be solved without guessing, and indeed some have more than one solution (depending on who made it and how diligently it was designed.)