A transmission actuator for a vehicle includes a housing, a first rocker for engaging a toothed wheel, a second rocker for rotating the first rocker to engage the toothed wheel, an engagement rod for rotating the second rocker, a solenoid arranged to displace the engagement rod, and a solenoid control circuit. The solenoid includes an iron core, a wire coil wrapped around the iron core, and a ferromagnetic plunger. The plunger is arranged to linearly displace in a first direction when a first directional current is applied to the wire coil, and linearly displace in a second direction when a second directional current is applied to the wire coil. The solenoid control circuit is arranged supply the first directional current when energized by a power source, and supply a decaying alternating current that includes the first directional current and the second directional current when the solenoid control circuit is de-energized.