Okay, we're talking Seneca being flown single pilot 135, with an autopilot exemption. Got it. From your description, you also rent the aircraft for outside use.
You can do all the instruction for outside rental you like, no restrictions, so long as the pilot whom you're checking out is legally capable of being PIC, if you don't hold a medical certificate.
If you are an instructor for your 135 company and do not hold a medical certificate (legal and permissible), you may provide instruction on the ground, in a simulator and in flight without holding a medical certificate, so long as you do not act as a required crewmember.
If you are in a single pilot aircraft providing instruction to a new hire pilot, you are not a required crewmember, even though your ops manual may require some specific instruction prepatory to a checkride. The instruction may be required, but you are not a required crewmember. You only become a required crewmember when you fill fly right or left seat in an aircraft requiring two crewmembers, or when you take on a responsibility such as SIC under 135 where a SIC is required by that part. In this case you do not need to be aboard, the instruction is conducted in accordance with Part 91 and within the certificate limitations of Part 61, even though the instruction is being used for Part 135.
You do not need the medical certificate. You are not acting as a required flight crewmember. Your training flights are not being conducted under Part 135. Your aircraft does not require a second crewmember. A medical certificate is not required under Part 135 to instruct, when not acting as a required flight crewmember. There should be no distinction between a new hire receiving initial flight instruction, and one who is already one the line receiving continuing flight instruction, as the FAA and regulation make no such distinction, insofar as who may provide that flight instruction.
Once the new hire is 135 qualified, I may even instruct on a revenue flight ("here's how we go into XYZ at night"), although I may not manipulate the controls.
As for your second paragraph, quoted above, as you're not a PIC or SIC and can't act as such without a medical certificate, you're not a company check airman, a representative of the Administrator, a representative of the National Transportation Safety Board, or a representative of the United States Postal Service, are you? If not, then when operating on a revenue flight, you still can't occupy that pilot seat. This is the case weather you manipulate the controls, or not.
Seems your POI is wrong on several counts.
§ 135.113 Passenger occupancy of pilot seat.
No certificate holder may operate an aircraft type certificated after October 15, 1971, that has a passenger seating configuration, excluding any pilot seat, of more than eight seats if any person other than the pilot in command, a second in command, a company check airman, or an authorized representative of the Administrator, the National Transportation Safety Board, or the United States Postal Service occupies a pilot seat.
§ 135.115 Manipulation of controls.
No pilot in command may allow any person to manipulate the flight controls of an aircraft during flight conducted under this part, nor may any person manipulate the controls during such flight unless that person is -
(a) A pilot employed by the certificate holder and qualified in the aircraft; or
(b) An authorized safety representative of the Administrator who has the permission of the pilot in command, is qualified in the aircraft, and is checking flight operations.
There is no difference between providing initial instruction for a new hire in your company Seneca, and one who is flying the line, with respect to your ability to do so without a medical certificate. Even though your operation and training program may require the instruction, the instructional training flight is NOT being conducted under Part 135, and even if it were, there is no requirement that you hold a medical certificate to provide that instruction.
Wherein lies the ambiguity?
