Although it has become a standardized practice nowadays to use randomized respawns, it is still extremely important to know where all of the spawn points are on every map. Every time you kill your opponent, listen carefully for the respawn sound. If you know all of the spawn points, you can use the process of elimination to narrow down where he might be.
At the nail gun
At the YA
Next to the water in the main room
Near the button in the RL area #2 (next to RA/100% area)