I agree with mindless1's point #2. What you describe really sounds like, at low engine RPM when the alternator output is reduced, electrical supply to your entire vehicle drops off. At higher revs it comes back. To test this, try other electrical devices under the same idle-versus-revved up comparison. I bet your windshield wipers do the same. If you have electric windows, same thing about how fast they move. At night you may be able to see this in the brightness of your headlights.
Three things could be involved.
1. Poor output from the alternator, and there are a few items in it that could contribute to this. But obviously it has not failed completely, because you get good electrical power (voltage) when RPM's are up.
2. Dirty / corroded electrical connections. IF the problem is isolated to only your fan, then examine its connections. If instead it affects several things, check through all the heavy cabling between the alternator, the battery, and the fuse boxes. High resistance at a contact point (e.g., corroded battery terminals and clamps) can interfere with delivering power.
3. Almost-dead battery. If your battery is really weak it can be difficult to charge up, and also it will not be able to deliver heavy current when there is no chaging happening at low RPM's.
Around here there are a few auto parts stores that will do a free test of your battery (some also will test the alternator) if you remove it from your truck and take it in to their shop. Testing usually takes most of a day, so you can't use the truck in that time. I'm always a little skeptical of what they say because they do these services to persuade you to buy a new one to replace the failing unit, but still it is useful info. And if the battery really is almost dead, there will be little doubt about that. So phone a few shops (if you don't already know about this service for free) and ask who does that.