The chirp is electrical. Try removing the BAT wire from the voltage regulator and insulating the bare terminal with a couple of wraps of electrician's tape, then do a test run or a short test drive on just battery power. Don't worry about draining the battery- - - -a well-charged battery should burn half a tank of gas or more before it gets too low to operate the ignition. Just dont run headlights, heater fan, etc. I'm going to bet the chirp goes away. It sounds like you need to adjust or replace the voltage regulator.
Jerry