1991 toyota corolla tail lights
The tail lights in my sister's '90s Subaru had a similar problem, and nobody could diagnose it, so she just kept a bunch of fuses in the car. (When she replaced a fuse, it would be a while before it blew again -- days, weeks or even months).
In your case, there's a continuous short circuit somewhere. I'd start with the tail lights themselves -- remove the bulb on one side, replace the fuse, then test. If the other bulb lights and the fuse didn't blow, you know the problem is in the wiring to the bulb you removed. If the fuse DID blow, replace the bulb, remove the bulb from the other light, replace the fuse and test again. Examine the wires carefully looking for nicks or bare insulation.
If the fuse fails whichever bulb is installed (or even if no bulbs!), then the short circuit is probably at the fuse box connectors for those wires, or inside the fuse box itself.
I assume you're talking about the tail lights that turn on and off with the headlights. If you're talking about the brake lights, the test procedure is the same, but don't forget about the high-mounted center brake light, if your car has one.