Have a 2002 Toyota Camry, I got a switch to disconnect the battery, but before that the battery would slowly drain if you left the car for about a week. The solution is fine for now, but how would I go about tracking down the issue, and why would it drain slow and not immediately if there was a short.
There a number of possible causes:
An old battery that can no longer handle the load of the "always on" accessories (clock, alarm, etc.).
A new load (like the inverter my son left plugged in) that is draining the battery.
A high resistance short that draws enough current to bring down the battery, but not enough to blow a fuse – a "short" is any path that short circuits the expected flow of current, they don't have to blow fuses.
A failed or failing component may be drawing more current that usual or preventing a load from turning off.
Here's how to troubleshoot:
Check for any obvious loads. Look for accessories plugged into 12 V outlets, trunk or glovebox lights left on, audio gear that doesn't automatically switch off, etc.
Verify that the battery is good (less than five years old, starter is cranks well and the car starts quickly – or have it tested, many auto parts stores will do this for you).
Check the top of the battery, if the top is dirty and especially if it is dirty and damp, there may be a high resistance path across the top of the battery. Clean it if in doubt. I don't think this is the problem in your case because the disconnect switch wouldn't prevent this one from discharging your battery. But in the general case this is the next thing to check.
Measure the draw on the battery when everything is (supposedly) off. Do this with an ammeter by disconnecting a battery terminal and reading between the terminal and the post on the battery. There shouldn't be more than a few tens of milliamps – anything approaching 100 would be very suspect.
If the draw is low, that points back to a bad battery. Have it tested even if you think it is good.
Assuming that you found a significant draw, the first thing I'd do is check again for anything that could be on when you think it's off (dome lights?). Then using the ammeter pull each fuse in turn and read with the meter across the fuse terminals. That will show you the load on all of the fused circuits. Keep track of the numbers, they should add up to what you got in the previous step. If they don't they you'll need to keep looking…
If you're not done yet, it may be worth finding a schematic or checking around the battery for additional fuses, then continue your search.
If you can't account for the draw that you see that probably means that at the problem is with an unfused portion of the electrical system. That means, most likely, the starter or the alternator or their wiring.