If it is one of the current bulbs that's causing the problem, maybe you could narrow the problem down to drivers' side or passengers' side by turning the headlight switch to the fully on position then switching your turn signal from side to side (to engage all bulb filaments) and see if the operation of either side blows the fuse instantaneously? Otherwise, disconnecting each individual connector like pb suggested would be a very good way to isolate the problem.

Are we to understand that you've simply been turning your lights on with no further activity (stepping on the brake pedal, etc.) and after a couple of minutes the fuse then blows? Stepping on the brake pedal brings other electronics into play like the high-mount led taillight section with it's own circuit board and suppression circuit.

Does the fuse blow out quicker if you adjust the illumination brightness knob on the dash? That could be an indication of problems with the solid state illumination controller.

You could also just make simple brightness comparisons side to side and front to back of similar type bulbs. A bulb with a filament getting ready to fail will usually burn brighter and brighter until the filament burns apart.