Let's suppose that a flight is being conducted under 14 CFR 135. The airplane is certified for single pilot operations, but two pilots who are both rated as PIC on the 135 certificate occupy the pilot seats. One of the pilots is a CFI. Does anything in 14 CFR 135 prevent the CFI from giving dual given time to the PIC while he flies?
It took me a little bit to figure out the underlying reason for asking this question and it has to do with logging flight time. For example, in a single pilot operation with an autopilot, the second pilot is not required and therefore cannot log the flight time at all even though their company may want them there. The FARs don't allow the second pilot to log the time.
The regulation that governs logging of flight time is 61.51.
61.51(h) Logging training time. (1) A person may log training time when that person receives training from an authorized instructor in an aircraft, flight simulator, or flight training device. (2) The training time must be logged in a logbook and must: (i) Be endorsed in a legible manner by the authorized instructor; and (ii) Include a description of the training given, the length of the training lesson, and the authorized instructor's signature, certificate number, and certificate expiration date.
So the question becomes what training was given during the revenue Part 135 flight and were you an authorized instructor?
The term Authorized Instructor is only found in Part 61.
61.1. Authorized instructor means— (i) A person who holds a ground instructor certificate issued under part 61 of this chapter and is in compliance with §61.217, when conducting ground training in accordance with the privileges and limitations of his or her ground instructor certificate; (ii) A person who holds a flight instructor certificate issued under part 61 of this chapter and is in compliance with §61.197, when conducting ground training or flight training in accordance with the privileges and limitations of his or her flight instructor certificate; or (iii) A person authorized by the Administrator to provide ground training or flight training under part 61, 121, 135, or 142 of this chapter when conducting ground training or flight training in accordance with that authority.
Since it is a Part 135 revenue flight I would believe the CFI would have to comply with section 135.338 and 135.340.
135.340(a) No certificate holder may use a person nor may any person serve as a flight instructor unless— (1) That person has satisfactorily completed initial or transition flight instructor training; and (2) Within the preceding 24 calendar months, that person satisfactorily conducts instruction under the observation of an FAA inspector, an operator check airman, or an aircrew designated examiner employed by the operator.
If the authorized instructor has complied with 135.338 and 135.340 they are also bound to the training program for the 135 company. If that training stipulates you can give dual given during revenue flights than you are more than welcome to do so. If there is no provision in the training program to provide instruction during revenue flight then it should not be done.
The best option is to request a legal interpretation on the validity of what you are wanting to do.
Short answer: NO
Long answer: In a flight where the CFI is certificated to provide instruction and the two are sitting in pilot seats then the PIC may log any part of that flight as dual instruction. It does not require the CFI to actually say a word in order for it to count as dual; even if he's merely observing, if something bad happens he'll open his mouth or take controls.
Part 135 is more about requirements for operations; it does not affect flight instruction, which is a part 91 regulated activity.