There are two stages of aux fans -- fast and slow.
The slow speed should generally always be on if your air conditioning is running. I don't know if your A/C is working or not, but in many if not most conditions, when A/C is running that low-speed fan should be running.
The fast speed (which you will definitely hear from outside the car, perhaps not inside the car on a W140) should kick on when the coolant temperature reaches 105-107 degrees centigrade. If the system is working correctly, when the fast speed fan kicks on, it should push the temps back down to around 90C.
The fast speed is independent of the A/C system's low-speed operation, meaning that the low speed and high speeds are controlled by different parameters. Put in other words, the fans can go directly from OFF to high speed; it is not dependent on having the lower speed operating first.
I don't know if you have checked the operation of your fan clutch, but this is another very important part of the cooling system, particularly for low-speed driving. There are threads here about how to check for proper operation of the fan clutch; this is best done in hot ambient temps (I would say 80F and above outside).
It is a concern that your fans are not working. There are two things I would immediately check are the fuses and relays, as it looks like you have begun doing. The fuses, particularly. It is not all that common for the relays to go out, so I would focus more on the fuses. I would just find the correct fuse(s) and replace them straightaway.
There are THREE coolant temperature sensors, and all are located in the front part of the intake manifold on the M119. One of them (the single-pole sensor) is specifically and only for the gauge on the instrument cluster. One of them (I believe the four-prong sensor) provides a direct input on coolant temp to the LH fuel injection system. And one of them (the two-prong sensor) is geared toward the fan operation. It is relatively common for these sensors to go out -- I actually had one fail on my G-wagen (M104 six-cylinder engine) that also prohibited the fan to operate.
It sounds to me like one or more of your coolant temp sensors have failed, to be honest. They are all inexpensive to buy, particularly if you go aftermarket. They are all located on the intake manifold as
per this post. All of the coolant temp sensors are accessible from the front of the engine and shouldn't require any disassembly to replace. It's important to get new crush washers when replacing them, however.
Another often overlooked item that is not often replaced is the thermostat. It's also inexpensive and not horribly difficult to replace, and a good idea if you don't know that it has been done. Thermostats can fail in several ways -- I have found that either they make the engine take a long time to come up to temperature from a cold start, or they allow the engine to get to very hot temperature more at high speeds and a bit less so at lower speeds (where the fan clutch and aux fans handle the bulk of the cooling). So while I don't necessarily think the thermostat is your problem, it probably wouldn't hurt to replace it with a Behr or Wahler unit.
Generally speaking (and I've lived in very hot climates like Houston, and in Portland OR, and now in Maryland), and I have had many vehicles with cooling systems in varying states of efficiency and condition.... a well-functioning cooling system should keep the temperature generally between 85-90C and 100C in all kinds of traffic. 90C is generally what you want to see. In very hot ambient temps (Houston, 95F in the summer with high humidity), you can see things creep up to 105C in stop and go traffic, but the fans and fan clutch should force those down quickly. In the Pacific Northwest, even in the summer, I believe that anything above 100C indicated on the gauge, would indicate a problem.
The flickering problem with your gauge could in my opinion either be a ground issue at the cluster, or a problem at the coolant temp sensor. I think the former is more likely. You'd have to pull the instrument cluster out of the dash and check all of the connections on the back of it to be sure. There's also an outside chance that the gauge itself could be bad, but the issue sounds more like an electrical connection relating to the wiring harness to me -- see next paragraph.
I believe it's the single-pring coolant temp sensor screwed into the intake manifold that goes to the gauge on the instrument cluster. Question -- has your
upper wiring harness been replaced? Are you familiar with the issues relating to these upper wiring harnesses? Does the wiring where it attaches to your temp sensors look OK, or is the insulation peeling from the ends of the wires? If that harness is bad, then it can lead to all kinds of problems. And the upper wiring harness contains the wires to ALL THREE of the coolant temp sensors.
If your harness has not been replaced, and is the original one for your car -- there is a very strong chance that this may be your problem. There is A LOT of information on the forum here relating to the upper wiring harnesses.
To be honest -- if you have not replaced your upper wiring harness, I would do that before doing ANYTHING else in terms of diagnosing your issues.
Good luck, and keep us posted on what you find. I'm sure that others with far more experience than I will chime in.
but man really be careful doing it because its not the safest thing to do (disclaimer... 
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