Instrument cluster
 

I am trying to figure out which wire on the back of the instrument cluster is for the temperature gauge. The wire running to the coolant temperature sensor is bright yellow but there isn't a bright yellow wire on the back of the cluster.

Alex, buy a manual from the self help section of O'Rielys or Autozone and look in it for wiring diagrams.
The sensor does not run the heat gauge.
The sensor sends information to a computor. The computor interprets that information and runs the heat gauge.
That is the purpose of the computor, to monitor sensors distributed through out the car and the run things. Todays cars it helps to have a book of some kind that tells you how and gives wiring diagrams so you can see this.

Yupper .................... buy the book.

I have 3 different books and none of them really help because they only show the earlier generation or the generation after mine. None of the 3 books show the generation my car is in. It irritates me that they are like that.

O.k., Can't help with that, Although there is a part of me that says pretty much if you have any thing that indicates wiring for a Saturn S series car that there stands a very good chance that there is little if any difference in major wiring of how the car runs as the series was pretty much in common with each other. The statement that the wiring from the sensor connects to the computor is going to be pretty much accurate as is the statement that the computor is connected to the gauge is probably true also and they are going to probably use the same wiring colors and basic configuration. Which leaves this question.
Why do you want to know this or what is it you are actually looking for because:
The sensor does NOT connect to the gauge.
The gauge is connected directly to the power train control module (one of the computors in the car) and uses 2D a dark green wire and 2E a black wire. The black wire connects to a ground bus running through the dashboard and thus to the negative side of the battery.

I am trying to wire up a coolant temperature gauge that sits in a pod. The instructions I got for it say use "senders mounting location" but never specifies where exactly to put it.

The information given is not enough to answer your question. Here is a URL of a temperature gauge installation instruction sheet.
http://www.egauges.com/pdf/AutoMeter/382g.pdf

It too is vague which is a problem also. It is used as an example to point out that a temperature gauge is generally supplied with a sending unit that has to be installed on the engine in some location where it can sense engine water temperature.
Assuming that a gauge will be able to use the same wire the automobile dashboard gauge uses is a false assumption for a veriaty of reasons. Mostly because different gauges will use different engine temperature sensor or in the case of computor controlled dash boards, the gauge is driven by a computor and all bets are off as to what kind of signal the gauge gets to create a display.
So I am guessing that if that is all the information given in the instructions I would have no idea where to hook it up to. My logic says it just don't work that way. There should be a sensor that goes with the gauge that has to be installed on the engine some where that senses water temperature.
And I have no idea where that would be on a Saturn engine. In fact I have to do that on my Mercury Marine engine I am installing in an autombile I am building and at the moment I do not know what I am going to do other than I do know this engine has a number of locations I can install a sensor in.
Thinking back I had to do this for a fuel injection conversion I did, the fuel injection needed to know the engine temprature and it came with a sensor that had to be installed. It turned out that the way to do it was to purchase a gauge adapter that installed in a heater hose line directly off of the location where the heater hose came off of the water pump of the engine and then the sensor screwed into the adapter. This adapter was a doorman product and I had a part number to give my favorite autoparts location (CarQuest) and I was able to buy that part from the auto parts store. But the instructions gave me a part number to do that with.
There should be a sensor supplied with the gauge and some further instructions.
Check for them. Also the name of the gauge manufacturer might help.
If what you wrote is all the instructions say! Then it is leaving the installation of a sensor (which you did not say was supplied) to you to figure out how to do it. The location for the heat sensor on a Saturn engine is on the cylinder head on the back portion of the head. The definition of back in this case where the engine sits sideways is the drivers side of the engine at the end. And I guess it is also assuming that some how you are either supplied with an adapter that takes both sensors so the dashboard gauge will work AND your Pod Gauge and I am guessing you have no adapter. Also that sensor tells the engine control compuor what the engine temperature is and it is extremely important to the engine computor that the sensor is installed correctly and is the proper sensor because it is critical to engine operation.
Dunno how to answer your question. Need further information.

To answer the original question only --> the wire you are looking for is dark green