Fuel Gauge and Temperature Gauge Dead

The instrument regulator is not connected to the ammeter (what you called the "battery gauge.)

It may or may not be that simple. On my own 67, there were a number of problems with the temp/ fuel gauge system.

I don't know that I'd buy an Autozone replacement, rather spend the bucks on an aftermarket solid state replacement. RTE is one

(I'm not connected, but they seem to be good)

http://rt-eng.com/rte/index.php/Main_Page

Again, there may be other problems.

Generally, the IGN switch feeds power to the cluster, to the warning lights (oil and brake) and to the instrument regulator.

The output of the regulator branches off and goes to both gauges,

and each gauge then goes to a sender to ground

On my 67, here are the problems:

The harness connector pins were in terrible shape, some broken and some corroded and loose. You can resolder them, mine were so bad I replaced the originals with Radio Shack "Molex" style connectors

The brass fingers which form the socket for the VR were not making connection to the PC board, and I had to solder jumpers between the brass fingers and the copper board traces.

The gauge nut studs were corroded. Consider replacing them with "real" nuts and work them loose/ tight several times to insure connection.

The senders for both gauges go BACK through two pins on the harness, so another place for trouble

The fuel sender wire goes down to the connector for the rear harness in the left kick panel, and back to the rear

The temp sender feeds out through the bulkhead connector, yet another source of trouble for that gauge.

I recommend you plan on getting dirty and doing it "right."

Pull the bolts on the column floor plate, drop the column, and (after unhooking the battery) pull the cluster out, and go through it methodically checking each point I mentioned.