Brokers take a break when they go broke
Seriously, with large brokers, they would have a large number of traders working at the same time who could take a break in rotation. For many, I guess the tea, breakfast (maybe even lunch) would be on the desk itself, with one eye on the terminal. Maybe the only real break they take is to answer the call of nature.
Don't know about the others but the dealers at the local Sharekhan take a quick lunch break at 3.30 and are back for afterhour trading.