Do you get a lower voltage like something between 8V and 10V? If so, that would suggest a weak battery or starter motor that is pulling excessive current.
If you get absolutely no voltage at the coil while cranking but you find 12V with the key sitting in the run position it really does point to the ignition switch. There is not a long list of things to look at. When you turn the key to the run position, the big brown wire feeding the ignition switch is connected to the white wire going to coil (+). When you turn the key to the start position, the big brown wire feeding the ignition switch is connected to the white wire going to coil (+) AND the white/red wire going to the solenoid.
As a sanity check you can try a couple of simple tests but be sure to reverse these things when done.
Disconnect the white/red wire from the solenoid and wrap the disconnected wire end with tape so it won't short. Have your friend turn the key to the start position again and measure the voltage between coil (+) and earth. If you do not find 12V, then there is a problem with the ignition switch. By removing the white/red wire you are insuring the starter motor cannot turn so there will be no drain on the battery that lowers system voltage. If on the other hand you find 12V on coil (+) while cranking with the white/red wire disconnected, this suggests a problem where the battery cannot deliver enough current and/or the starter may be in need of refurb.
Another test can be made by TEMPORARILY running a wire from the starter solenoid (where all the brown wires are) directly to coil (+). That will immediately put power in the coil, bypassing the ignition switch. If you turn the key to start and the engine fires up, the problem must be in the switch. NOTE: With this jumper wire in place you will have to pull the jumper wire back off the solenoid to stop the engine. Since the jumper bypasses the switch, turning the key off will have no effect.