Energy Source for Gamma Rays from Merging Neutron Stars When the two neutron stars merged in the latest event, large amounts of gamma rays were emitted.  Given that their deorbitting is a result of gravitational wave production, where does the energy for the gamma rays come from?

The only sources I can think of are the rotational kinetic energies of the merging stars or the potential energy released by the final collapse into a single spherical mass.
Not Nuclear fusion;
There is also a huge amount of nuclear fusion that creates heavy elements from all the iron there is in neutron star: they in fact are not only made of neutrons. But as said in comment, building of heavier elements rather consumes energy than it generates some.

Not sure scientists  has a clear agreement on how this works. 

Gravitational collapse

For example I found this (rather old) abstract which states it could be a result of gravitational collapse, without singularity (since here the result of the merger might not be a black-hole, or the lightest ever: around 2.7 solar masses!)


  theoretical developments (string theory, quantum gravity, critical collapse), which suggest that complete gravitational collapse can occur without singularities or event horizons 


Thermonuclear event again: fission

From Space.com, they say Kilonova energy could be explained by rapid atomic decay of heavy elements


  The mergers of dense cosmic bodies that are thought to cause short gamma-ray bursts can also blast out neutron-rich gas that rapidly generates heavy elements such as gold and platinum, scientists say. These "r-process" elements can undergo radioactive decay and release an enormous amount of energy — 1,000 times or so that given off by stellar explosions such as novas. These powerful events are thus known as "kilonovas"