Very true those inline fuse holders cause no end of problems.
The best thing to do is get rid of those archaic inline fuse holder and install a small blade fuse box which is readily available anywhere and far more reliable.

I would still confirm that your fan is working. Checking with a heat gun shows that it can still switch but NOT that it is doing so at the right temp. I have had a few issues with these over the years. Most recently it came down to dodgy in-line fuse. The ones that sit behind the intake on the firewall. Those will cause all sorts of gremlins. What tends to happen is that they heat up and the plastic starts to melt slightly and over time, the connection point recesses back to the point where it is no longer...or maybe just barely making contact with the glass fuse. My fan would come on but sometimes later then it should, not at all or run for far too short a time. 

So, do yourself a favor and check the condition of those inline fuses. All of them. Then be sure to clean and lubricate all connections for corrosion. The fan switch sits right at the front of the car and get corrode pretty fast if not checks often.

Usually the switch in the rad goes bad. You say the head gun trips the switch for continuity but at what temp. Try a pan of boiling water, which is 212 degrees. If you have all the fuses and relay working ( relay up by the wiper motor ), then wire the fan to a interior manual switch.

I'm embarrassed.  We went ahead and ordered a new fan switch, I just installed it today.  To replace it, you have to dump all the coolant.  When we topped it back off, it never overheated.  I guess the system just had an air bubble.

Hey all, I'm new here.  I have a classic mini with a SPi engine setup.  I've recently run into some overheating problems at idle, which i'm almost 100% positive is the Auxiliary fan not turning on.  My dad and I trouble shot the wiring harness and traced it back to what we thought was the fan switch.  We unplugged the wires from the switch and jumped them and it ran the auxiliary fan just fine.  We also checked the relays and fuses and haven't found any faults there either.  However, when we let the car idle and get up to temp, the auxiliary fan never kicked on.  We took the fan switch out and put it under a heat gun to check for continuity, and sure enough, the switch works fine.  Does anyone have any idea what might be going on here?  Thanks!