Yes, the ignition circuit is on when the key is in the start position and in the run position. As mentioned above, the ignition run wire from the switch goes through a resistor wire, full battery power to the coil during start is via the yellow wire from the starter. As soon as the key is released from the start position the yellow wire no longer provides voltage. There will still be voltage potential at the yellow wire on the starter as it is connected to the coil and the ignition wire from the key, but it dead heads at the starter when the starter is not engaged.
Terminals on the ignition switch are: Ground, Ignition, Battery, Solenoid (starter), and Accessory. With the key in the OFF position only the Battery terminal is HOT. When key is in Start, the battery terminal connects to the Solenoid and Ignition terminals. All three are HOT. When the key is in Run, the battery terminal connects to the Ignition and the Accessory terminals. All three are HOT. When the key is in Accessory, the battery terminal connects to the Accessory terminal. Both are HOT.
Power for your headlights, horn, four ways, brake lights, dome light, etc. are independent from the ignition switch, they get power from the main splice. Only accessories such as the radio, and in your case it seems, the tach light are powered through the ignition switch. That's why if you have the radio on when the car is running and you turn the ignition off the radio also shuts off. as soon as you start the car or turn the switch to accessory the radio comes back on. Other circuits tye in to the ignition switch, such as signal lights, heater, A/C, wipers, brake warning light, etc.