Your emergency fund should be large enough to cover emergency-level spending for the few days it takes money to transfer from your brokerage to your checking account. In theory, this could be one day if you did a wire transfer.
Emergency spending might include a hotel, car rental, clothing and hygenie purchases, a prepaid phone, various fees, a few days of restaurant food, and a few hundred dollars for medical copays.
Some people say why have ANY idle cash? Get a credit card for emergency situations and pay if off in a month from brokerage proceeds. This is a big debate.