Battery charging probs with a DSC alarm

I have an old DSC PC 500 security alarm. One day it started beeping with a low battery. So I bought a new 12V battery and replaced the old one. A few days later, it starts beeping again. Thinking it was a faulty battery, I replace it again. The same thing happens. I did some research and it appears these old DSC alarms are prone to their charging circuits failing. This is super annoying because the alarm won’t function without a charged battery, even when it has full AC.

Here’s what I did to solve this: I bought a “BatteryTender” trickle charger and hooked the alarm leads AND the trickle charger alligator clips to the battery simultaneously. That way, if the AC is ever cut, the alarm’s AC AND the charger’s AC will both shut off and the battery will work as intended. But while there is AC, the trickle charger should keep the battery charged without harming the alarm, thereby avoiding the low battery signal.

It’s a tight squeeze, but here’s what it looks like: