When using nanosecond repetitively pulsed discharges to actuate on dynamic combustion instabilities, the environment the discharge is created in is unsteady and changing on the timescale of the combustion processes. As a result, individual discharge pulses are triggered in a background gas that evolves at the timescale of combustion dynamics, and pulse-to-pulse variations may be observed during the instability cycle. Prior work has studied nanosecond pulsed discharges in pin-to-ring configurations used to control instabilities in lean-operating swirl-stabilized combustors, and observed variable discharge behaviour. The focus of this work is on characterizing how the pulse-to-pulse discharge morphology, energy deposition, and actuation authority, evolve during the combustion instability cycle. This has important implications for designing effective plasma-assisted combustion control schemes. The discharge is observed in two distinct modes, a streamer corona and a nanosecond spark, with the occurrence of each regime directly linked to the phase of the combustor instability. Variation of pulse repetition frequency affects the total fraction of pulses in each mode, while variation of voltage affects the onset of the nanosecond spark mode. The transitions are described in terms of ratios of the relevant combustion and plasma timescales and the implications of this coupled interaction on the design of an effective control scheme is discussed.