'How is it possible to recognise an extended period of oratio obliqua unintroduced by a verb of speech in Tacitus?'

One obvious indicator that a passage of Latin is indirect speech is an absence of indicative mood verbs, though of course writers like Tacitus might often use infinitive and subjunctive verbs as the primary verbs of an oratio directa sentence for stylistic purposes. Thankfully in Tacitus a lot of the unintroduced oratio obliqua is in the form of questions, so if you look out for 'an' or 'quid' when struggling on a passage you should assess whether translating the passage as indirect speech would be appropriate. In particularly extended oratio obliqua there is usually a combination of infinitives and subjunctives which should suffice to demarcate it from directa. Shorter unintroduced obliqua must be discovered by context- a person coming to speak before the suspected passage is a good indicator and in that circumstance an indirect translation should always be considered.