I think Brinsley chose death over prison for shooting his girlfriend, and decided to kill some police officers before he died, out of hatred and the desire for posthumous glory.
Mentally ill, wired wrong, but not insane by legal standards, deliberately choosing evil for himself and the world.
I suspect if he could have gotten on a train immediately he wouldn’t even have killed himself; he probably watched one pull out and realized he wouldn’t make it out (otherwise he could’ve offed himself right there on the sidewalk).