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Thank you for allowing me to assist you, my name is Joe and I will be happy to assist you with your concern today.
3 wires usually include a hot, hot with key on and a ground, it's very possible that however they were spliced that one of the wires came loose esp if those tap connectors are used where you press them together to connect wires together. Your best option is to remove the splices and only have the radio wires connected and nothing leftover from removing the other component, however what you will be looking for is loose/disconnected wires. The only difference here will be from the ignition switch itself though (between key on and backwards to acc) both supply key on 12v to the radio, the other hot is hot at all times and the ground is just that, this means that you usually have a problem at the ignition switch not the wiring, however start by checking the harness, wiring and connector to the radio.
You will have two hot wires, one hot at all times and the other is your key on hot, this is the one you will want to use your voltmeter in checking.
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