The mass of the 99% comes from (kinetic?) energy that quarks have as the come together to from a neutron. This system has some energy like a rope moved by standing wave. Standing wave is a sum of waves traveling back and forth and sometimes adding up and sometimes cancelling each other into nothing.

Gluons pop up out of nothing to carry this energy that struggling bound quarks have and add up into nothing passing their energy back to quarks.

If you pump in even more energy into this system (for example by smashing something into it) even something like new quark-antiquark pair can pop up into existence and one of the original quarks might fly off away with one of the new particles to form a separate meson. The other particle from the created pair stays and changes the identity of three quark particle so it's no longer a neutron but some other three quark particle.

The mass comes from binding energy, not kinetic. The binding energy is potential energy in the gluons and their interactions with the quarks.

Isn't binding energy, the energy released when things bind? And energy that has to be delivered to the system to break it apart? [1]

The energy that is present withing the system of bound components must be something else.

[1] https://en.wikipedia.org/wiki/Binding_energy