Gauges that have quit working can cause a lot of frustration and inconvenience. It's disconcerting to find that you don't know how hot the engine is running, if the oil pressure is low (when equipped with a gauge), or how much fuel you have to make it to the service station. The gauges in your 70 mustang all work the same way. Diagnosing the problem is at most time consuming but not a task that is too difficult for the mechanically minded.
Your fuel, oil, and temp gauges operate in the following manner.
The ignition switch on the column provides power when turned on to a black with green striped wire which goes from the switch, into the main harness where it turns into a violet wire wihich goes to the instrument panel or cluster connector. The violet wire at the end of the connector is the one that feeds power to the instrument voltage regulator through the printed circuit board (shown below). From there, the regulator sends a pulsing signal to the gauges at their hot post. The gauges then ground through the other post to their respective sending units. You can use a test light to see if the voltage regulator on the back of the cluster is sending a pulsing signal to the gauges or check the sending units and see if their connector is pulsing. That other violet wire toward the center of the connector is for the dual brake warning switch. Sometimes that can get confusing.

INTERESTING NOTE: When using a test light on a non-tach instrument cluster, the pulsing signal is strong on the left inner posts on the fuel and temp gauges with the weaker pulse detected on the right or outer posts. The oil gauge is backwards. The stronger pulse is detected on the right outer post with the weaker pulse on the left inner post.

If they have all gone out at once, either power has been interrupted to the voltage reg from the cluster connector or ignition switch, the regulator is bad, or in some cases, one or more gauges may have shifted where they are mounted and the hot post is touching the metal housing opening.
Each gauge in your cluster, except the speedometer and tachometer if equipped, should be installed so that the two posts on the back of each gauge are centered in the rectangular opening in the metal housing. The brass nuts holding the gauges in place are meant to hold them centered and connect them to the printed circuit board. If the cluster has been apart and the gauges were not installed properly, sometimes the gauges can shift in their opening. If the hot post of a gauge touches the metal housing, it will cause that gauge or others to stop working. If the ground post is touching, then when you turn on the ignition, that gauge will suddenly read all the way on the gauge. There are small rectangular stiff cardboard inserts that are supposed to be slipped over the gauge posts to help hold them centered while the printed circuit board and brass nuts were installed and to insulate them from the metal housing. These can become loose fitting or get lost over time. The best way to verify the gauges are centered after the printed circuit board is installed is to unplug the Constant Voltage Regulator, then, using an ohmeter, test continuity between each gauge post and the metal housing. If you get a reading, then a gauge post is possibly touching the edge of the opening and will cause problems. What could be worse is if the ammeter gauges shorts against the housing. There could be some sparks then. :-) Sometimes it's a bad or worn ignition switch. You might try slightly turning the key and see if they come back on.

So, in review, the circuit for the gauges is:

Ignition switch, cluster connector, instrument voltage regulator, gauges, sending units. There isn't much to it. Now of course there can always be broken wires, broken runners on the printed circuit board, or bad components. Usually however the gauges themselves prove not to be the problem, just something in the circuit somewhere.

The printed circuit boards of these clusters should be replaced with new ones if possible. Over time, these get fragile but mainly the two plastic sheets that hold the runners can separate. This leaves open the possibility of accidental shorts or runner breakage. "In the old days," jumper wires were just soldered across breaks to complete the circuit. Also the runners at the harness connector can become loose and move out of alignment causing mysterious bad connections. A new circuit board will eliminate this problem.