Replace fuel gauge - 2005 Harley Davidson FLSTN- FLSTNI Softail Deluxe

There is a capacitor that evens out the voltage from the fuel tank sender unit. This would typically be on the gauge display unit.

Or there is a bad connection, so check the wiring connector on top of the tank.

It appears to be a known issue

https://www.google.com/search?q=ISUZU+KB+250D+fleetside+fuel+gauge+not+stable

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If the tail lights, low fuel light, temperature gauge, and fuel gauge are not working, there could be several possible causes:

1. Blown Fuses: Check the fuses for the tail lights, low fuel light, temperature gauge, and fuel gauge. If any of these fuses are blown, replace them with a new one.
2. Loose or damaged wiring: Inspect the wiring for the tail lights, low fuel light, temperature gauge, and fuel gauge. Look for any loose connections or damaged wires. Repair or replace any damaged wires and ensure all connections are tight.
3. Faulty sending units: The low fuel light and fuel gauge are connected to the fuel sending unit in the gas tank. The temperature gauge is connected to a temperature sending unit on the engine. Check these sending units for faults, and replace them if necessary.
4. Faulty instrument cluster: The instrument cluster itself could be faulty, causing the temperature and fuel gauges to not work. A qualified mechanic can test the instrument cluster to see if this is the issue.

It's also possible that the trike has a separate electrical system for the tail lights, and that this system is malfunctioning. A qualified mechanic can test the trike's electrical system to determine the cause of the issue.

Fuel gauge sensor in the fuel tank

Not much point replacing the fuel pump until the supply and ground has been checked and found to be ok.
Gauge sender might share the same ground...

If the fuel gauge sender and fuel pump share the same space, replacing the pump provides the ideal opportunity to test the gauge unit with an analogue ohm meter.

Are you sure its not the fuel sending unit and not the fuel gauge itself.Because the sending unit controls the fuel gauge level and if the float gets stuck then the fuel gauge will not work.

This is a normal concern.
The instrument cluster uses 4 different operating modes to calculate the fuel level:
Anti-slosh (default mode)
Key OFF fueling
Key ON fueling
Recovery
After a fuel fill up, the time for the fuel gauge to move from empty (E) to full (F) ranges from 2 seconds to 55 minutes depending on which operating mode the fuel gauge is in.
The default fuel gauge mode is called the anti-slosh mode. To prevent fuel gauge changes from fuel slosh (gauge instability due to changes in fuel sender readings caused by fuel moving around in the tank), the fuel gauge takes approximately 55 minutes to go from empty (E) to full (F).
The key OFF fueling mode (2 seconds to read empty [E] to full [F]) requires 3 conditions be met:
The key must be in the OFF position throughout the entire refueling of the vehicle.
At least 15% of the vehicle's fuel capacity must be added to the fuel tank.
The instrument cluster must receive a valid key ON fuel sender reading within 1 second of the key being put into the RUN position. The key ON sample readings are considered valid if the fuel sender reading is between 15 ohms ± 2 ohms and 160 ohms ± 4 ohms.
If these conditions are not met, the fuel gauge stays in the anti-slosh mode, which results in a slow to read full (F) event.
The key ON fueling mode (approximately 90 seconds to read empty [E] to full [F]) requires 3 conditions be met:
The transmission is in PARK (P).
The key is in the RUN position.
At least 15% of the vehicle's fuel capacity must be added to the fuel tank.
In key ON fueling mode, a 30-second timer activates after the transmission is put into the PARK (P) position (automatic transmissions). When the 30-second time has elapsed and at least 15% of the vehicle's fuel capacity has been added, the fuel gauge response time is 90 seconds to read from empty (E) to full (F). When the transmission is shifted out of PARK (P), the fuel gauge strategy reverts to the anti-slosh mode. The key on refueling mode prevents slow to read full events from happening if the customer refuels the vehicle with the key in the RUN position.
Recovery mode is incorporated into the instrument cluster strategy to recover from a missing fuel level input during a refueling event. Missing fuel level inputs result from intermittent opens in the fuel sender or its circuits. Recovery mode (empty [E] to full [F] approximately 20 minutes) is initiated when the following 2 conditions are met:
The instrument cluster is in the anti-slosh (default) mode.
The actual fuel level in the tank is greater than what is being displayed by the fuel gauge

the fuel meter gauge inside the fuel tank is not work frequently,chek the fuel meter gauge,ok