I just bought 2009 Roughhouse 50, and the fuel light stays on. The dealer says this is hard wired dash light, not a low fuel level warning indicator .... True or false?

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 .

I suggest you read the vehicle owner's handbook to be certain what the exact function of the light is. You will need to know that in order to determine whether the light is warning you or is broken.

The fuel light usually warns the fuel level in the tank is low...

Principles of Operation
NOTE: When installing a new instrument cluster, the new instrument cluster must be configured. Refer to Section 418-01 .
The instrument cluster is a hybrid electronic cluster (HEC) which receives and outputs information using both hardwired circuitry and the controller area network (CAN) communication circuits.
It is very important to understand:

• where the input originates from.
• all the information necessary for a feature to operate.
• which module(s) receive(s) the input or command message.
• if the module that received the input controls the output of the feature, or if it sends a message over the CAN to another module.
• which module controls the output of the feature.

The instrument cluster carries out a prove-out when the ignition switch is turned from the OFF to the RUN position to verify the integrity of the warning indicators. The charging system warning indicator, the low oil pressure warning indicator and the malfunction indicator lamp (MIL) illuminate when the key is turned to the ON position, and then turn off when the engine is started. The seat belt warning indicator proves-out for 60 seconds and then turns off, or turns off when the seat belt is fastened. The following indicators prove-out when the key is turned to the ON position:

• door ajar warning indicator (3 seconds)
• anti-lock brake system (ABS) warning indicator (3 seconds)
• O/D OFF indicator (3 seconds)
• air bag warning indicator (6 seconds)
• brake warning indicator (3 seconds)
• door ajar warning indicator (3 seconds)
• shift up indicator (3 seconds)
• low fuel warning indicator (3 seconds)
• traction control indicator (3 seconds)
• check fuel cap indicator (3 seconds)
• passive anti-theft system (PATS) indicator (3 seconds)

Low Fuel Warning Indicator
The instrument cluster utilizes fuel level data supplied by the hardwired fuel pump module to control the low fuel warning indicator, which illuminates when the fuel drops to a pre-determined level.
Your best bet is to take this to the Ford dealer , unless you have Ford IDS - factory scan tool to diagnose this
Your best bet

The red square shaped warning dash light is an image of a crudely drawn radiator indicating that you are low on coolant. Topping up your coolant bottle reservoir located on the passenger side above the wheel should clear up your issue. If your coolant level is full and is still indicating low coolant via dash warning light, you could possibly have a sensor out in the radiator or air bubbles in your coolant lines that need to be bled out.

Whenever this warning light or any other stays on in the dash it is indicating that the systems control module (or the system sensor in the case of lights like low oil pressure, door open indicators etc.) has detected a fault, it then disables the system (this applies to ABS,TCS, and SRS) as long as the light is on. You must now have the dealer hook up a special electronic diagnostic tool and "scan" the system for the fault code that is stored for the problem(s)

instructions:

1 Turn the ignition key to the "II" position.

2 Check the lights on the dash. You should see a variety of dash lights light up. One of those lights will be a "Check engine" light. This light should stay lit with the ignition key in the "II" position. The rest of the lights should go out. If the "Check engine" light begins to blink, you may have a problem with one of the vehicle's electronic components. Consult your owner's manual or call your dealership for possible servicing issues.

3 Start the engine. The "check engine" light should go out after a few seconds. If it does not, this can indicate either a maintenance interval has been reached or a more serious problem with the vehicle's emissions control system. Again, it is advised to consult your owner's manual or call the dealership for service.

4 Check for an illuminated "SRS" light on the dash. The SRS light indicates a problem with the supplemental restraint system, i.e., the airbag, on the Camry. This needs to be serviced by a professional mechanic.

5 Check for an oil light on the dash. The oil light is in the shape of a small oil canister. When this lights up, it indicates low oil pressure. Low oil pressure is caused by a blockage in the system, a weak oil pickup or oil pump, or low oil levels in the engine. Check and see if your Camry is overdue for an oil change. It is recommended that the oil be changed at 5,000 miles or every six months.

6 Check for the low fuel warning. The fuel light on the Camry is on the fuel gauge near the "E" on the gauge face. The low fuel light means that you have to refuel your vehicle.

7 Check for the seat belt warning light. The seat belt warning light is a picture of a figure wearing a seat belt. If your seat belt is unbuckled, then this light will illuminate (along with a warning chime) indicating that you should buckle up.

8 Check for an orange car with lights on (on the dash lights). This warning light indicates that one or both of your brake lights has failed, or the electrical resistance in the bulb filament indicates that it is about to fail and will need service soon.

BMW PARTS

Hi , there will be 3/4 wires at the fuel tank gauge. 1 ground wire ,1 gauge(on dash) wire, 1 gauge low level indicator light (warning on dash) Get a test lamp , ground test lamp and probe each wire. 1 will do nothing (earth wire) 1 will bring on dash low fuel light , the other will be the gauge on the dash which will rise (slowly) to the full position.

1. Brake warning light:
   This light functions for both the parking brake and the foot brake systems.
2. Parking brake indicator: When the ignition key is in the ON position, the light comes on when the parking brake is applied.
   1. 1. Check the brake fluid level. Add brake fluid as necessary. See .Brake fluid. in the .Maintenance and do-it-yourself. section of this manual.
      2. If the brake fluid level is correct, have the warning system checked by a NISSAN dealer.
   2. Low brake fluid warning light: When the ignition key is in the ON position, the light warns of a low brake fluid level. If the light comes on while the engine is running with the parking brake not applied, stop the vehicle and perform the following:
3. Low tire pressure warning light (if so equipped)

If your vehicle is equipped with a Tire Pressure Monitoring System (TPMS) that monitors the tire pressure of all tires except the spare. The low tire pressure warning light warns of low tire pressure or indicates that the TPMS is not functioning properly.

I’m happy to help further over the phone at https://www.6ya.com/expert/jeremy_69f3cc28d95bf514

Is the emergency brake on???

Are you sure the coolant is still low in the bottle. The coolant sensor thats in the bottle has a float that can stick. If it sticks the low coolant light will stay on even if the coolant level is right. Try tapping on the coolant reservoir bottle in the area where the electrical wire enters it. Not too hard. If that is the porblem the light should reset.