Iirc Hexum’s gun was loaded with blanks. He held it to his temple not realizing the explosive pressure from the blank was enough to send a piece of his skull through his brain.

More info from the wiki

On October 12, 1984, the cast and crew of Cover Up were filming the seventh episode of the series, “Golden Opportunity”, on Stage 18 of the 20th Century Fox lot. One of the scenes filmed that day called for Hexum’s character to load cartridges into a .44 Magnum handgun, so he was provided with a functional gun and blanks. When the scene did not play as the director wanted it to in the master shot, there was a delay in filming. Hexum became restless and impatient during the delay and began playing around to lighten the mood. He had unloaded all but one (blank) round, spun it, and—simulating Russian roulette—he put the revolver to his right temple and pulled the trigger, unaware of the danger.[8]
The explosive effect of the muzzle blast caused enough blunt force trauma to fracture a quarter-sized piece of his skull and propel this into his brain, causing massive hemorrhaging.[3][9]