There is no provision or FAA definition of flight time with regard to the position of the landing gear, and that has no bearing on your logging of flight time, nor on your flight time limitations under Part 135.

Always think in terms of your duty or liability. You have a duty to operate in accordance with the regulation, which defines flight time as the time commencing when the aircraft moves with the intention of flight until it comes to a rest after landing. This same definition will determine your flight time with respect to Part 135 flight time limits, and will be considered if there is ever a mishap and an investigator looks at the flight, duty, and rest times leading up to the mishap.

If your employer uses hour meter time which is activated by an air switch, oil pressure, squat switch, or other means, that's your employers responsibility with regard to tracking time for maintenance; it's an owner/operator responsibility. You are responsible for your flight time, however, and must account for it when considering your limitations under Part 135.

14 CFR 61.51 spells out the regulation regarding the logging of flight time.