Ignition Switch, Mitsubishi Fuso

Currently im working on Mitsubishi Fuso truck that has a problem starting. It does not get 12V on the start with the key but the ign and the acc get 12V so i am figuring maybe the ignition key cylinder is bad. Though, so the owner of the truck doesnt have to go through buying another cylinder with new keys, i want to put a button instead so he could continue using the same keys with his broken cylinder and could save a bit of money himself. Instead a buying a seperate button to start the car, i want to put a relay to a button that the car already has like the horn or something similar. So how would i wire a relay up so i can start the car by the push with button but still having the security of having the keys in the ign cylinder in order to start the car?

By the way, there is only a constant 12V, an acc wire, a starter wire, and an ign wire.