In the sutta (MN 28), the phrase "right time" is in the translation of kālaññū which is defined in dictionaries here ("one who knows the proper time"), and here.
Kālaññū knowing the proper time for ... (c. Dat. or Loc.) Sn. 325; described at A. IV, 113 sq.; as one of the five qualities of a rājā cakkavattī (viz. atthaññū, dhamma°, matta°, k°, parisa°) A. III, 148; one of the seven qual. of a sappurisa, a good man (=prec. +atta°, puggala°) D. III, 252, 283; as quality of the Tathāgata D. III, 134=Nd2 276; Pug. 50.
The most complete explanation of kālaññū that I found in the suttas is in Dhammaññūsutta (AN 7.68).
The definition in that context is:
And how are they one who knows the right time? It’s when a mendicant knows the right time: ‘This is the time for recitation; this is the time for questioning; this is the time for meditation; this is the time for retreat.’
In that sutta it's one of seven qualities:
A mendicant with seven qualities is worthy of offerings dedicated to the gods, worthy of hospitality, worthy of a religious donation, worthy of veneration with joined palms, and is the supreme field of merit for the world. What seven? It’s when a mendicant knows the teachings, knows the meaning, has self-knowledge, knows moderation, knows the right time, knows assemblies, and knows people high and low.
Of these seven, the quality with the longest description is the last (I abbreviate slightly in the quote below):
And how are they one who knows people high and low? It’s when a mendicant understands people in terms of pairs. Two people:
- one likes to see the noble ones, one does not.
- one likes to hear the true teaching, one does not
- one lends an ear to the teaching, one does not
- one remembers the teaching they’ve heard, one does not
- one reflects on the meaning of the teachings they have remembered, one does not
- one understands the meaning and the teaching and practices accordingly, one understands the meaning and the teaching but does not practice accordingly
- one practices to benefit themselves but not others, and one practices to benefit both themselves and others
That’s how a mendicant understands people in terms of pairs.
The definition of "one who knows assemblies" might be relevant too:
And how are they one who knows assemblies? It’s when a mendicant knows assemblies: ‘This is an assembly of aristocrats, of brahmins, of householders, or of ascetics. This one should be approached in this way. This is how to stand, to act, to sit, to speak, or to stay silent when there.’ If a mendicant did not know assemblies, they would not be called ‘one who knows assemblies’. But because they do know assemblies, they are called ‘one who knows assemblies’. Such is the one who knows the teachings, the one who knows the meaning, the one who has self-knowledge, the one who knows moderation, the one who knows the right time, and the one who knows assemblies.
There's a discussion on SuttaCentral at the moment, ‘Qualifications’ neccesary to teach Dhamma? There someone said that the situation e.g. relationship with a teacher is different within the Sangha: I recommend this answer (which I won't quote here) and the answer immediately following that.