What brake was it? I don't think draining it will achieve anything more than flushing it through without draining it.
Ultegra. Something is wrong as air seems to get into it quickly. No obvious leaks though.
You won't achieve nothing emptying the system and filling it again. I won't even bother to replace the fluid if it's freshly bleed. Just use the cup and remove any air, if it losses pressure over time there's definitely a leak somewhere.
@atz started
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What brake was it? I don't think draining it will achieve anything more than flushing it through without draining it.