Q: Relay for engine management doesn't work unless the magnetized plate is pushed in. Please help!

Generally speaking, there are two separate circuits inside of a relay. One circuit is, what I’ll refer to for the sake of this writing, as the "supply" side, and the other is the "signal" side. The supply side has a positive and negative post, and is what supplies voltage to the component being controlled, by way of the switch inside the relay. The signal side also has a positive and negative, but the signal side is what actually commands the switch inside the relay to close, and allow voltage to flow through the supply side. This is the reason there is typically four posts on a relay.

If you have to manually push the switch closed to get the circuit to work, then something is keeping the supply side from getting the signal necessary to close, and allow voltage to flow through the supply side. Without knowing the model of the vehicle, I’m not sure if the computer controls the voltage, or the ground, to complete the circuit.

You would need to get a wiring diagram and test the individual pins in the fuse box to see if there is a voltage or ground signal that isn’t being supplied when commanded. Once you figure out what signal is being received, then you have to figure out why. These situations are where a certified mechanic becomes valuable. If you would like to have this taken care of, a certified professional from YourMechanic can come to your car’s location to inspect the electrical system and proceed with the proper repairs.