Sounds like you're on the right track. A 2AMP draw is enough to drain the battery in a day or two.

These magic boxes are typically impossible to troubleshoot, but since it is a short, you might get lucky with the module on the bench and an ohmmeter connected, disconnecting the obvious components that might be causing the short. These components would be such things as diodes and other possible voltage regulator components.

Anyone familiar with electronic components could do this and you might get lucky. Without schematics it's somewhere between difficult and impossible to go any further.

Good luck,