wierd happenings

My 1993 del sol has a wierd problem can anyone help ? The clock starts to blink , the lights flash off and on ,and a clicking sound is on the inside , and the red light on the consol flashes . If i turn the lights off and on a couple times it stops . When i turn off the ignition , the syptoms continue till I start it back up and go through the light off and on cure stops it . I have run the battery down a few times and had to replace the alternator ( whew that was fun ) . Anyone know what it is or how to fix it . Thank you

Do you have an alarm system installed by chance?