No, the amorphous trait doesn't interact with the Squeezing rule.
Rules only do what they actually say, and you're reading something into the rule that isn't there.
"Squeezing into a Smaller Space" says
A creature can squeeze through a space that is large enough for a creature one size smaller than it.
It doesn't say "you can squeeze to fit through a hole half the size you'd normally need". It only talks about creature sizes. A medium creature with Amorphous is still medium sized, so the squeezing rule only applies to spaces that a Small creature can pass through without squeezing (in which case Amorphous lets you do the same thing without taking the penalties for using Squeezing, so you can pretty much just ignore squeezing entirely).
Whatever size your character is, if you see a 1-inch hole, amorphous says you can use that opening. If you see a 3/4-inch hole, it's too small for amorphous. Squeezing doesn't care about that, it only says "Is it big enough for a creature one size smaller than you?"
I think the easiest way to think of this is a little like having two armor class calculations available. You can only use one of them at a time, so when it comes up, you pick whichever one is more useful in that particular circumstance. If you decide to use Amorphous, then you aren't squeezing. If you decide to squeeze, then you aren't using Amorphous.
Now, you could get into an odd situation with this. It's certainly possible that you could be playing a halfling or kobold who has gained the Amorphous trait and then casts Reduce to become Tiny, or you could have a Rat familiar that has somehow become amorphous (gross), at which point there actually isn't a size category smaller than Tiny for the squeezing rules to reference. In this case, for an opening of an inch or larger, you don't need to worry about it because amorphous clearly works, but for smaller openings, it's largely up to the DM to decide whether the creature can squeeze through. However, if the DM decides they can get through it by squeezing, Amorphous is irrelevant to that; a non-amorphous rat familiar or Reduced kobold could get through it anyway.
Of course, your DM might decide differently and allow you to use Amorphous AND squeeze at the same time to get through even smaller openings. But by the rules as written, for most player-character purposes, an amorphous (or similar) creature never needs to squeeze, because they have another ability that's superior in every way.