Very good. For 45 cents at Mouser you can get a ULN2803 8-channel Darlington Array that can turn Arduino 5V to up to 500 mA of 50V (or 12V) = with built-in back EMF protection= given up to 50V (or 12V) external power capable of the load and a a heat sink on the chip. You need 2 channels for your shift toggles. That leaves 6.<...>
The shift solenoid valve resistance should measure 19-24 ohms minimum when measured at 20°C (68°F). The shift solenoid current flow should not exceed 0.75 amps. The shift solenoid should energize at a voltage of 7.5 volts or more (measured across the terminals). The shift solenoid should de-energize when the voltage is one volt or less.