How do you change the set time players respawn? I'm not sure which entity/output would fix it. I've tried tf_gamerules, but no output options seem to indicate setting the re spawn time to a different amount of seconds.
I believe respawn time changing is done through the Set<Team>TeamRespawnWaveTime input to the tf_gamerules entity, with respawn time being respawn wave time -> 2*respawn wave time
It's a little more complicated than twice the set value. It is both the minimum wait time and the time between spawn waves. Since it's the minimum time, players will never be assigned the next spawn wave, but rather the wave after the next wave.
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