All 4 terminals will have 12V on them when the guage has power. Resistor goes verticle (horizontal on fuel gauge). Pink wire connects to two coils inside the guage, one coil connects between pink and green wires and is grounded thru the temperature sender. That coil moves the guage upscale towards hot. Second coil connects between the pink wire and the top terminal, then it runs thru the 86 ohm resistor to ground at the bottom terminal. This coil moves the gauge downscale towards cold. Gauge that goes hot and does not return to cold indicates a bad ground on the back of the gauge, a guage that never moves off cold indicates an open in the temperature sender circuit. could be anywhere from the pink wire terminal to the sender itself. Measure the coil resistance from the power terminal to the green terminal and from the power terminal to the top terminal make sure neither is open circuited, also make sure neither is shorted to the case (although if they were you should blow your instrument panel fuse).
Following up on Mark's information, refer to the following link: http://www.camaros.org/forum/index.php?topic=4227.0
In this discussion at the above link, there are two post with PDF file attachments which are pages 3-241 and 3-242 from the National Service Data TUNE-UP MANUAL; 1961-1969. These two pages (PDF attachments) provide trouble shooting procedures for Chevrolet (not just Camaro) gauges along with a good schematic representation of all the gauges including the temp gauge.
The temp gauge schematic and troubleshooting guide is contained in the second attachment, page 3-242.
The calibration resistor is referred to on page 3-242 as the "A" coil or the coil on the left side of the temp gague schematic. Needle position on the gauge depends on the current flow through the "A" coil to ground (cal resistor) vs. current flow through the "B" coil and the temp sending unit to ground. Current flow through the "A" coil is essentiially constant. Current flow through the "B" coil varies and is controlled by the change in the internal resistance of the temp sending unit which varies with engine temp.
As I understand it, and if everything is working as it should;
1) If you disconnect the green wire at the temp sending unit, then there is no current flowing through the "B" coil. In this case, the needle will stay pegged left on the gauge at the "C" position.
I have previously checked this on my 69 RS with the engine at normal operating temperature, needle on temp gauge inidcating normal tem. As soon as I disconnect the lead at the temp sending unit, the needle goes to "C". Reconnect the lead at the temp sending unit and the needle moves back to indicate normal engine temp. If the gauge is constantly reading "C" this would indiicate either no voltage to the gauge or an open somewhere in the green line between the gauge and the temp sending unit or the temp sending unit itself is open and defective.
2) If as soon as you turn the key to the "ON" position; applying 12v to the gauge, the needle deflects all the way to the "H" position, then there is no current flowing through the "A" coil - which is either caused by an open cal resistor or bad ground at the bottom terminal.
What you are experiencing may well be an internal issue in the armature of the gauge itself, in which case a new guage may be the solution.