Yes on C4's there is a normal draw down on the battery, but it is very small, and even after a week or two would only draw off the batteries surface charge.
Unfortunately a lot of electronics are actually "on" all the time, in the so called standby mode, c/w soft touch switches.
At home on the mains, whats a few extra watts on the bill, day in, day out.
The problem can be exacerbated by the circuits used, a broken earth connection, can cause all manner of illogical wierdo stuff.
I have a Rhino alarm on my 87, left on it flattens the battery, so its only switched into circuit when Miss Muffit is on board.
She likes the facility of the keyless remote access to BOTH doors. Besides the OEM alarm is quiet satisfactory.
You need a multimetre - one that reads DC current, cct diagram, time , patience, isolate one cct at a time. Probably start with the ones playing up.
But remember to disengage the OEM alarm, to avoid false leads.
Not sure on a 91 but modern electronics use microprocessor chips to retain settings and memories, today "Super Capacitors" can hold a charge for months, this holds info in memory. Electrolytic Capacitors have a habit with heat and time to either dry out and go open circuit, or boil their guts out and/or explode, the mess cooks & shorts or eats away other components.
You need to get an "Electrical diagnosis service manual Supplement". This is a GM book, breaks the ccts down, is very explanitory, good value.
OR - a good serviceman. (This option also requires a fat wallet)