The only place to look for Fiat answers is:
http://www.mirafiori.com See you there.
Your back taillight dim issue can be fixed with a decent
ground wire (will solve the typical "semi-bad fuel pump" problem too). After 25 years, solder on the rivets to get better connection is also typical. The dim headlights can be solved with the
"brown wire" to the ignition switch trick (adding current flow around the OEM wiring). You can do both in under an hour and the above site has lots of details. Fiat, in its infinite wisdom, is not much into solid ground circuits.
A 124 should run right at 190 degrees F (directly up on your temp gauge) and your electric fan will come on at just under 200. From a cold start it will take at least 20 minutes to idle up this temp. Underway, you will be hard pressed to overheat the thing and any sort of downhill will produce a slight cool down. Learn to burp the air out of it and 99% of your problem will be gone. This system partially diverts water to the cold side rather than pumping it around with a blocking thermostat like most cars. Read up on it at the above link.
There is nothing on this car that can not be fixed by someone with basic skill, plus the parts are dirt cheap. I just got my '81 as a teaching aid to my own young driver but I had forgotten how much damn fun a 2 litter coupe could be. On the other hand, the going price from perfect to junk is perhaps 6k to 2k.