I wish I could help considering I caught one, but it was completely by accident and I don't even know what I did. And of course it was in my second town that I barely started. I can't seem to catch one in my main.
Just keep fishing. Fish, and fish, and fish. Look for the larger shadows in the stream. I caught mine by complete accident too when I was fishing up near the top of my town.
Gar are biiiig shadows, and finding one is really just up to luck :[ Like others have said, keep at it, but don't get too burned out (I didn't fish for a long time once after binge fishing for another rare species). You're sure to catch one sooner or later!
In my towns,I usually find the big river fish near the bridges.The AC Wiki says the gar is found in the river pool but the ones I've caught this summer were near a bridge.
You probably know that they're river fish, and their shadows are really big. I think they might be starting to go out of season too though, so that might be another explanation.