I admit I can't play for very long now, but do not ever recall having to empty my third slide on a trumpet, but sure some would on longer sets.
But, there is remedy...
When the valves are in the open position the spit could be blown quickly out the first valve slide if removed, or a water key placed either on the slide or the last knuckle.
Playing a double horn I often had to clear the leadpipe, and very occasionally one of the F side slides (usually the third)...but I never had to empty the B-flat side valve slides.
Horns are notorious water P-traps...so, I would guess a water key might also he advised in this case either on the last knuckle or the third valve slide.