Here is the updated schematic. I tested the circuit out using batteries and diodes. I was concerned that the diode in the enable lead (dark blue) of the buzzer might cause the buzzer not to sound. That was not the case. I haven't checked this out in the car, but the information I have about the way the ignition switch operates indicates to me it should work.
One note - the wires coming from the buzzer are awfully skinny - looks like 30 AWG or smaller. If it were me, I would mount everything inside a "hobby box" - you can get this at Radio Shack" and have more robust wires, 20 AWG or so, coming out of the box and use those wires to tap into the MGB's wiriing harness.
As to cost, the buzzer was about $10.00 and a package of 25 1N4001 diodes was about $2.50