What causes my temperature gauge go from high to low

Do you mean the engine is overheating?
Few modern engines will tolerate overheating without sustaining damage and often one incidence of overheating is enough...

Localised overheating often causes cracks in castings and always causes distortion of metal.

While it is possible the temperature sensor is faulty and sending incorrect temperature information to the computer that drives the gauge, there are conditions where a healthy sensor can send low temperature messages about an engine that is overheating.

To be accurate the sensor must be immersed in coolant so a low coolant level can result in a low reading and similarly a failing head gasket will cause gas bubbles in the cooling system that will rise to the top of the engine, displace coolant, interfere with the thermostat operation and overwhelm the degassing circuit.

It is important you get the problem diagnosed and sorted.

No , their arn't two coolant temp. sensors . One near the thermostat housing . The Temp sensor is a input to the PCM / ECM . The PCM / ECM needs the temp info for fuel calculations . The temp gauge on the instrument cluster gets this info over class 2 serial data network Hooking up a factory or professional scan tool that can read sensor data is the easy way to diagnose ,not guessing . Looking at factory service info. an wiring diagrams too see what is what is another way . You have no clue ,take it to a qualified repair shop.

The engine coolant temperature sensor is a thermistor (a resistor which changes value based on temperature) mounted in the engine coolant stream. Low coolant temperature produces a high resistance (100,000 ohms at -40°C/-40°F) while high temperature causes low resistance (70 ohms at 130°C/266°F).
The PCM supplies a 5 volt signal to the engine coolant temperature sensor through a resistor in the PCM and measures the voltage. The voltage will be high when the engine is cold, and low when the engine is hot. By measuring the voltage, the PCM calculates the engine coolant temperature. Engine coolant temperature affects most systems the PCM controls.
The scan tool displays engine coolant temperature in degrees. After engine startup, the temperature should rise steadily to about 90°C (194°F) then stabilize when thermostat opens. If the engine has not been run for several hours (overnight), the engine coolant temperature and intake air temperature displays should be close to each other. A hard fault in the engine coolant sensor circuit should set DTC P0117 or DTC P0118; an intermittent fault should set a DTC P1114 or P1115. The DTC Diagnostic Aids also contains a chart to check for sensor resistance values relative to temperature.
The ECT sensor also contains another circuit which is used to operate the engine coolant temperature gauge located in the instrument panel.

Replacing a fuel pump has nothing to do with instrument cluster lights or the clock staying on. Unless you shorted wires , did you disconnect the negative battery cable before hand ?
The body control module (BCM) performs the following functions:
• A/C compressor request
• A/C cooling fan
• Exterior and interior lighting control
- Daytime running lights (DRL)
- Automatic lighting control
- Fog lamps
- Interior lighting
• Battery rundown
• Chime
• Gauge control
• Instrument cluster indicator control
• Fuel gauge control
• Temperature gauge control
• Theft deterrent
Interpreting all of the driver warnings sent by the control modules on the class 2 serial data line
Sending the information to the instrument cluster in the form of a SPI serial data bus message
The following list of messages are sent by the BCM to the instrument cluster:
• Fuel gauge position
• Temperature gauge position
• Oil pressure
• Low engine coolant
• Check oil
• Volts
• ABS
• High beam
• Low fuel
• High temperature
• Washer fluid level low
• CRUISE
• BRAKE
• SERVICE VEHICLE SOON
• Door ajar
• Seat belt
• THEFT SYSTEM
• PRNDL
Check the fuel level sensor wires , the fuel level sensor is a input to the BCM .

Reasons the Temperature Gauge Reads High

If the temperature gauge reads high, it could mean your engine is overheating. Another reason your reading might be high is you could be losing coolant. A small leak or evaporation may cause your radiator to slowly lose coolant. A third reason your temperature gauge reads high could be because the thermostat is broken. If this is the case, you may need a coolant temperature switch replacement. The last reason the temperature gauge could read high is because of a water pump, or water pump gasket failure. If the water pump is malfunctioning, it may need to be replaced by a professional.

What to Do If Your Temperature Gauge is High

If your temperature gauge is reading high, it means your car is overheating. This is a very serious matter and you should never drive an overheating car. If your car starts to overheat, shut off the air conditioner and open the windows immediately. If this does not reduce the overheating, turn on the heater as high as it can go. If this still doesn't work, pull over on the side of the road, turn off the engine, open the hood carefully, and wait until the vehicle cools down. Never open the radiator cap while the engine is hot - coolant can spray and burn you. Once the vehicle has cooled, take the car to a mechanic right away so they can diagnose the problem. Cars are especially susceptible to overheating in hot climates, like what's common in cities like Los Angeles, Phoenix, Las Vegas, or Atlanta.
The temperature gauge is an important tool in your vehicle that shows the temperature of your engine's coolant. Contact YourMechanic and have your car inspected for overheating if it reads too high, as this can cause serious problems...

Reasons the Temperature Gauge Reads Cold

On most vehicles, the temperature gauge reads cold until the engine has run for a few minutes. If the temperature gauge still reads cold after the engine has warmed up, the gauge may simply be broken. Another reason the temperature gauge could read cold is if the thermostat in the vehicle stays open. With the thermostat stuck open, the engine can be overcooled, causing a low temperature reading. If this is the case, the thermostat may need to be replaced.

The PCM regulates voltage to the coolant fan relays, which operate the fans. Refer to Engine Controls.

Engine Cooling Fan Description - Electric
The electric cooling fans are used to lower the temperature of the engine coolant flowing through the radiator. They are also used to cool the refrigerant (R-134a) flowing through the A/C condenser.
Operation
The electric cooling fan operates when the engine cooling temperature exceeds a certain value. The cooling fan on this engine is controlled by the PCM. The cooling fan has one speed. The PCM turns the cooling fan ON by grounding the coil of the cooling fan relay when certain conditions are met. When the A/C is requested, the cooling fan will also be turned ON.
Power for the cooling fan motors are supplied through Cool Fan #1 and Cool Fan #2 relays. The cooling fan relays are energized when current flows from the fuses in the Cell 23: Cooling Fan Controls , and through the relay coils to ground through the PCM. The Low Speed fans control circuit is grounded for low speed fans operation. During low speed fans operation, both fans run at a slow speed. The High Speed fans control circuit is grounded for high speed operation. During high speed fans operation, both fans run at high speed.
Important: When certain Diagnostic Trouble Codes (DTCs) are present, the PCM may command the cooling fans to run all the time. It is important to perform Powertrain On Board Diagnostic (OBD) System Check prior to diagnosing the engine cooling fans.
If a problem that involves the low speed cooling fan relay control circuit exists, DTC P0480 should set. If the problem affects the high speed cooling fan relay control circuit, DTC P0481 should set. A problem with the ECT sensor should set DTC P0117, P0118, P1114, or P1115. Any of these DTCs will affect cooling fan operation and should be diagnosed before using the Cooling Fan Diagnosis tables. The Cooling Fan Diagnosis tables should be used to diagnose the PCM controlled cooling fans only, if a DTC has not set.

The engine coolant temperature (ECT) sensor (3) is a thermistor, a resistor which changes value based on temperature, mounted in the engine coolant stream. Low coolant temperature produces a high resistance (100,000 ohms at -40°C) (-40°F), while high temperature causes low resistance (70 ohms at 130°C) (266°F).
The PCM supplies a 5 volt signal to the ECT sensor through a resistor in the PCM and monitors the terminal voltage. Since this forms a series circuit to ground through the ECT sensor, high sensor resistance (low temperature) will result in high PCM terminal voltage. When the resistance of the ECT sensor is low (high temperature), the terminal voltage will be drawn lower. This terminal voltage indicates engine coolant temperature to the PCM.
A hard fault in the ECT sensor circuit should set either a DTC P0117 or P0118. Remember, these DTCs indicate a malfunction in the engine coolant temperature circuit, so proper use of the DTC table may lead to either repairing a wiring problem or replacing the sensor, to properly repair a problem.

The engine coolant sensor is an input to the PCM , Two wire's both go to the PCM .An the PCM turns on the cooling fans !

DTC P0480 Cooling Fan Relay 1 Control Circuit
DTC P0481Cooling Fan Relay 2 Control Circuit
The Body Control Module (BCM) request the cooling fans. The BCM sends a Class 2 message to the PCM in order to enable the fans based on various inputs. Thebattery voltage travels to all three cooling fan relay coils. The PCM enables cooling fan relay #1 by providing the ground path. The PCM enables cooling fan relays #2 and mode control together by providing a ground path. The left and right cooling fans are connected in series. This will enable both fans on low speed when the fan #1 relay is energized. When all three fan relays are energized, both fans will operate at high speed. The high speed is possible because the fan relays are wired in a parallel circuit. When the PCM detects that certain DTCs are set, the PCM will enable the cooling fans.
The PCM will enable the engine cooling fans when certain Diagnostic Trouble Codes are set.

Important: A short to ground will cause an open fuse(s). Before performing this diagnostic procedure, inspect the fuse(s) for an open.
1
Did you perform the Instrument Cluster System Check?
--
Go to Step 2
Go to Instrument Cluster System Check
2
Turn the ignition switch to the ON position.
With the scan tool select Instrument Panel Cluster, Special Functions, Instrument Panel Cluster (IPC) gauges.
Perform the Coolant Gauge Sweep Test.
Does the coolant temperature gauge complete a full sweep when commanded?
--
Go to Powertrain On Board Diagnostic (OBD) System Check in Engine Controls
Go to Step 3
3
Replace the instrument cluster. Refer to Instrument Cluster Replacement .
Did you complete the repair?
--
Go to Instrument Cluster System Check
--

Your best bet would be to take your vehicle to a qualified repair shop that knows how the system works . An has the tools to diagnose the problem .

Changing gears and the temp gauge have nothing in common. First, check the coolant level. If gets low an air pocket in the engine will cause the gauge to go high, then back to normal. Next would be to check the wiring. could be the gauge/sensor wire is shorting to ground.

Make sure coolant level is as it should be. If level is low look for evidence of leak(s). Top off fluid if necessary. The engine coolant temperature sensor is a very common issue with these vehicles and may be the cause of your issues if no leaks are found. Also a faulty thermostat cans cause the sensors to read voltage high but most likely a sensor issue. The sensor is a potentiometer (variable resistor). The computer sends 5v through one of the wires this voltage goes through a resistor which will vary the voltage based on temperature sensed by the engine coolant temperature sensor. The sensor has a negative temparature coefficient meaning the resistance will go down when temperature is high and up when temperature is low. The less resistance the more of the 5 v gets back to the computer. The PCM detects this high voltage and set the check engine light on warning you of an issue. Whe this sensor goes bad it is usually accompanied by temperature gauge fluctuation or erratic operation and the cooling fans run long or all the time even though the vehicle is cold. Hope this helps.

Sounds like you have installed a 'over-temperature switch' type sender unit- this type of sensor is only meant to control an over-temperature alarm indicator lamp that is either 'on' or 'off'.

The temperature gauge requires a 'variable resistance type' temperarure sensor to control the meter deflection.
When cold the temperature sensor is of high resistance, hence less meter deflection;
when hot temperature sensor is of low resistance, hence more meter deflection.

You need to procure a matching sensor to suit the type of gauge installed.

Is it possible you have connected to the temperature wrong temperature sensor? - most vehicles are fitted with both a gauge type (variable resistance) sensor to drive the temperature gauge, as well as a switch type (on or off) sensor to drive the overtemp indicator light.

Since there is no voltage applied with the ignition off, if the gauge is not dropping down all the way, it is the gauge that has failed.
Temperature sensors are frequent failures but they are not active when the car isn't powered up. They can be intermittant, high, low but with no power, the gauge itself should go to the minimum.  

The Engine Coolant Temperature (ECT) sensor is mounted in the intake manifold and sends engine temperature information to the ECM. The ECM supplies 5 volts to the coolant temperature sensor circuit. The sensor is a thermistor which changes internal resistance as temperature changes. When the sensor is cold (internal resistance high), the ECM monitors a high signal voltage which it interprets as a cold engine. As the sensor warms (internal resistance low), the ECM monitors a low signal voltage which it interprets as warm engine.
Fig. 1: View of the Engine Coolant Temperature (ECT) sensor Fig. 2: Engine Coolant Temperature (ECT) sensor locationTESTING
See Figures 3 and 4

1. Remove the ECT sensor from the vehicle.
2. Immerse the tip of the sensor in container of water.
3. Connect a digital ohmmeter to the two terminals of the sensor.
4. Using a calibrated thermometer, compare the resistance of the sensor to the temperature of the water. Refer to the engine coolant sensor temperature vs. resistance illustration.
5. Repeat the test at two other temperature points, heating or cooling the water as necessary.
6. If the sensor does not meet specification, it must be replaced.

Fig. 3: Intake Air Temperature (IAT) and Engine Coolant Temperature (ECT) sensor wiring diagram Fig. 4: ECT sensor temperature vs. resistance values