Welcome to the forum! Us Buellers are mostly a do-it-yourself crew and willing to help the less tool familiar owners among us. Sounds like you 'checked everywhere before asking'
so I googled the words in your thread title and got "about 1,340,000 results in .34 seconds" LOL
Here ya go new guy. Happy you got a bike you like
RTFM: here's a free service manual download for you if you want to fix it yourself
There is a whole step-by-step section on how to check the fan.
http://buellmods.com
But since the fan isn't supposed to just 'turn on after every ride'*, you may not even have a problem.
I'll paraphrase the manual if you don't want to bother clicking that link I gave you:
Check for power at the fan. 2 wires. One is always powered (even key off) and turned on by the ECM grounding the other wire to complete the circuit... through the Fan Relay (#2)... that is available everywhere as A/C relay for some Ford. (Autozone) Duralast Pt # 19283... from this site... on this thread:
https://www.buellxb.com/forum/showt...erence-thread/page5&highlight=cross+reference
You should have power at one of the fan wires and it should run if you ground the other wire. Also easy to test all the sensors (including the temp sensor) with the free program ECMDroid (GooglePlay store). You will need a bluetooth dongle on the bike to connect your android phone or tablet to the ECM. I like the one I got from Buelltooth.com. ECMSpy and TunerPro work well too, and you'll need a cheap cable to connect to your laptop.
Also: Is it oily/wet? Seeping rocker box gaskets are common on a 14 year old motorcycle. If the engine is leaking oil on the electric fan. Electric things don't like to be oily things.
Parts are obsolete!?? Oh NO!! WHAT TO DO!? You have internet access? Google "Buell parts" and places to get parts (like E-bay or Harley Davidson) will pop right up. For
any old used motorcycle parts, Ebay, facebook, craigslist. For brand-spanking-new Buell parts, SPHDonline.com, Newcastle Harley, EBR, LAP.
TBH there are a couple very minor parts that are getting harder to find for such an old bike, which is true for ANY old bike, but stick around with enthusiasts of that brand (like BuellXB.com) and theres always a work around. Buell didn't make most of the service parts themselves. Bearings, tires, belts, bulbs, fuses, sensors, are all made by other companies so don't
assume you can't find them without even looking
*The fan is controlled by temperature (and sometimes speed controlled if that option is activated). So 'not turning on after a ride' is not a sign of any problem. The temp fan on/key off settings are usually lower and thats why it
usually acts that way. If your engine temp is lower than that setting the fan has no reason to run after a ride. All of those settings are easily checked or changed with the ECMDroid program.