If its a half wave rectifier, just put it in line with the AC to the fan. If its full wave, you connect the rectifier input across the AC and gnd, and the output to the fan, but the DC output ckt MUST remain isolated from any chassis gnd. The keep things simple on the bars, switch the AC input to the rectifier rather than the DC out. Just like the non-floating gmd DC lighting option discussed many times.
My wife's 250 Pampera has the same setup as the trials bikes, not sure if its full or half wave and its not handy to look. I seem to think its full wave but with no regulator. I could tell immediately from a schematic. How may terminals are on the device?
You could go one step up and get a Trail Tech rectifier/regulator. Regulated 12VDC output at the full rating of your 2K-3 stator. This would allow adding isolated DC LED or HID lighting in the future.