My 1969 Firebird has the same problem. When you put the key in the ignition lock, the key push on a little pin that operates a little switch (example picture: https://www.amesperf.com/parts/46740/) that sets off the buzzer. In my case, the pin seems to not move back after it has been pushed in by the key. I have tried to solve it once, but it involves taking the steering wheel off, then the plate for the steering wheel lock to get to the lock cylinder and the switch. It worked a little while, but then started to act up again. My solution so far has been to disconnect the plug on the horn relay/buzzer (on the firewall). If I remember correctly there are two plugs on the relay/buzzer. I mean, one plug for the horn relay function and another for the buzzer function, so you can disconnect the buzzer and still use the horn.