They ___ on the beach while my brother ___ on the phone.

The sentence describes two simultaneous actions in the past. The first action, 'They ___ on the beach', is in the past continuous tense because it describes an ongoing activity. The second action, 'my brother ___ on the phone', also describes an ongoing activity happening at the same time. Therefore, both verbs should be in the past continuous tense. 'They' is plural, so it takes 'were sunbathing'. 'My brother' is singular, so it takes 'was talking'.

Answer: were sunbathing / was talking