Battery Draining, vibrating needles

Looking for help here. My '81 does not seem to want to hold a charge. After a few days without the tender on it, the battery will be dead. Previous owner told me the clocks were notorious for draining the battery.I find that hard to believe. Here's why; the car has an aftermarket security system installed (from previous owner), besides the butcher job they did not replacing panels and screws properly. There is the curious issue of my gauge cluster. When the car is at idle the oil, water and ammeter gauges vibrate erratically. However as soon as the gas pedal is pressed all the gauges level out to normal readings. I'm suspecting some kind of short or bad connection. I don't think it's the security system or the clock just draining the battery. Should I start by checking and cleaning the battery and frame grounds? Has anyone else had similar issues? I appreciate any advice and help.

a guy i know has an 81 and he says his battery goes dead too. i believe your 81 had a computer controlling parts of it and that maybe doing it. the reason i say this is i have an 81 caddy. it was the first year for computer and this car eats batteries. besides me checking for shorts, others have checked and could not find one either. if i use the car no problem but if i let it set it kills the battery.

if you do have a short a way to narrow it down is as follows. make sure everything in car is turned off. you have to either do this with the door closed or make sure the door switch is kept in so lights are off. remember the clock (if working) will show a short in this so you may want to pull fuse. disconnect the positive cable on battery and use a continuity meter between the battery post and cable. if short is present you will get a reading. then just pull out a fuse and see if the reading drops. if not you know it's not that circuit and push that fuse in and go the the next one.

hope this helps.