By looking into the inner workings of PCGen, I have manage to cobble something together that seems to do the trick. However, this answer is in no way comprehensive, but meant to serve as a guide on how to patch your own homebrew stuff. For more information about working with Homebrew files, I suggest looking into the documentation (*Help -> Documentation*, <kbd>F1</kbd>), under the "List Files" heading (Sadly, I cannot link to specific pages of the documentation here).

Open up `[PCGen]/data/pathfinder/homebrew/my_homebrew`. This is the pre-installed Homebrew Campaign Thingy, which will do just fine for this purpose. 

Traits are internally handled as "abilities". Using a good text editor (Notepad++ or similar), open up `my_abilities.lst`. Under `#insert your data here`, add the following line

    Homebrew Trait		KEY:Trait ~ Homebrew Trait		CATEGORY:Special Ability	TYPE:Trait.BasicTrait.CombatTrait	PREMULT:1,[PREABILITY:1,CATEGORY=Special Ability,Trait ~ Homebrew Trait],[!PREABILITY:1,CATEGORY=Special Ability,TYPE.CombatTrait]		DESC:You have studied the workings of PCGen and managed to claw your way into creating a homebrew trait|PRERULE:1,DisplayFullAbility		NATURALATTACKS:Claw,Natural.Weapon.Melee.Finesseable.Piercing,*2,1d4

Let's look at this line more nicely formatted:

    Homebrew Trait
      KEY:Trait ~ Homebrew Trait
      CATEGORY:Special Ability
      TYPE:Trait.BasicTrait.CombatTrait
      PREMULT:1,[PREABILITY:1,CATEGORY=Special Ability,Trait ~ Homebrew Trait],[!PREABILITY:1,CATEGORY=Special Ability,TYPE.CombatTrait]
      DESC:You have studied the workings of PCGen and managed to claw your way into creating a homebrew trait.|PRERULE:1,DisplayFullAbility
      NATURALATTACKS:Claw,Natural.Weapon.Melee.Finesseable.Piercing,*2,1d4

1. It starts off with the name of the ability, "Homebrew Trait"
2. Next up is the `KEY` keyword, followed by the internal name of the trait, allowing you to use this trait in other homebrew things, as a prerequisite for a feat, for example. I followed the naming convention I found in other `*abilities.lst` files.
3. The `CATEGORY` tag is there to list this under *Special Abilities*, nothing much to say here.
4. The `TYPE` tag is more involved. This is a dot-separated list of subcategories this *Special Ability* falls under. In this case, we have a trait which is a basic trait, and which is a combat trait. You can change the latter to what you like, but you'll have to change the prerequisites as well.
5. The line starting with `PRExxx` denotes prerequisites. `PREMULT:1` states that only one of the following prerequisites need to be fulfilled. The prerequisites are given in square brackets.
  * `PREABILITY:1,CATEGORY=Special Ability,Trait ~ Homebrew Trait` means that you qualify for this trait when you have this trait. In particular, it means 1 prerequisite ability from the *Special Ability* category, which is "Trait ~ Homebrew Trait". This is needed because of the second prerequisite.
  * `!PREABILITY:1,CATEGORY=Special Ability,TYPE.CombatTrait` means "Not 1 *Special Ability* pf the `CombatTrait` type, as per the trait rules. Without the first prerequisite, this would make the trait disallow itself.
6. `DESC` is followed by the full description of the trait. Not sure what the `PRERULE` part does, just keep it there. 
7. Finally, `NATURALATTACKS` adds the crunch. I copied this part from a Tiefling Alternate Racial Trait. It adds an attack called "Claw", lists the applicable types (see above), makes it 2 attacks, and sets the damage to 1d4.

Once you have written up your ability to your liking, save the file and open up PCGen. Go To *Sources -> Select Sources* (<kbd>Ctrl</kbd><kbd>L</kbd>), and go to the *Advanced* tab. In the dropdown list at the top, select Pathfinder RPG as your *Game*. On the right side, you should now see "Pathfinder RPG for Players", as well as "My Pathfinder Campaign". Click on *Load*. Your homebrew trait should now be available to choose from the list of traits.