A and B got into an accident. A was driving a rental car, but his name
was not on the agreement.

BACKGROUND: B was making a left turn on a yeild signal  ( a signal
without a LEft turn signal but one can turn if it is green and clear)
just when the signal turned from Orange to REd and A was coming from
front trying to get the signal.

1. Who is at fault?
2. If B is, would the rental company go after its customer or B?
3. If A wants to take B to small claim court, who has a better chance/

Please not that the person who rented the car was not in the car, and
the driver was not suppose to be driving that car. No police report
was written.

Thank you.

Both are probably at fault.  The person turning left did not see the
intersection was clear to proceed and A did not obey the traffic
light.  The rental company will follow the path of least resistance. 
they have access to the credit card of the person renting car A and
likely have the contract in their favor as well as the law depending
upon the State. Injury, especially serious injury to one of the
parties could change the actions and opinions of the rental company
and all respective insurance carriers. Insurance carriers could also
be swayed depending on the seriousness of the injuries.

1. I would say A would be at fault as he/she did not obey the signal.
You can run a green/orange light, but never an orange/red light, you
either have refused to stop or was going too fast to stop (faster than
allowed)
Furthermore I think A was never allowed to drive the rental car and
therefore is not insured.
2. in the eyes of the carcompany, A and the person who rented the car
are the ones responsible because if A made use of the car, with SHARED
responsibility with renter, and wrecked it. The company will hold BOTH
persons responsible. (but if B is, then they will go after the
insurancemoney of B as the rentalcompany pays A's fare and will get
(no)claim)
3. I would say to A, you ran a red light!