Fuel gauge dropping to e saying low fuel when tank is half full

Fuel gauges are not meant to be precision instruments. You might want to fill up a 2 gallon can and drive the car until it runs out of fuel to see how low the gauge will go before it's really empty. Use the 2 gallons to get back to a filling station.
I once spent three working days trying to get a 1972 Chrysler to read full when it's full, half when it's half and quarter tank when the tank has a quarter amount of fuel. The customer did not want to accept anything else, but in the end all I did was to get close, not exact.
It is possible that the fuel float in the gas tank is "drowned", that is, the plastic float might have a slow leak and some fuel found its way inside. This will cause the float to submerge slightly and give you a low reading. To check this you will have to remove the float unit from the tank.
In any case, if you feel up the job (not easy) remove the float unit from the tank and manually move it up and down while checking the meter reading. You can bend the wire holding the float to correct misreadings.
Personally, I wouldn't bother, just be aware that when the reading is low, feel safe that you still have enough fuel to get to the next filling station.

clean the coil in sender unit

One of the wires to the sensor is touching a ground. It may be getting pinched

If the trouble with the gauge started after you worked on it then you likely damaged or created a restriction to the movement of the sending unit. You will have to remove the tank and double-check your work.

Its very simple. If the gauge is showing half full then fill the tank and see how much fuel it takes. If the amount you add is approximately 50 percent of the fuel tank capacity then you know the fuel gauge is accurate . In that case the computer is giving an inaccurate reading and should be ignored. All you need is an accurate fuel gauge - it does not matter a row of beans what the computer says if the fuel gauge is reading correctly.

hi it can really only be two things, first is the fuel sender on the pump inside the tank it could be stuffed or sticking causing a false reading, second it can also be a faulty fuel gauge on the dash.

Did the mechanic use an OEM replacement unit or an after-market unit? I think the original unit has a damping circuit to prevent immediate response when accelerating/stopping/cornering; the needle reacts slowly to changes in fuel level. If the new unit shows an immediate transient response, but settles back down to the actual fuel level, I'd just live with it.

Youre gauge is controlled by a plunger in the fuel tank which is attached to the sensor and the fuel gauge. it sounds like when the plunger goes down half way its either getting stuck down lower then it should. Needs replacing. Any mechanic can do this install for you.

You have to drop the tank, on your fuel sending unit if the "float" that tells the gauge how full your tank it. These like to get holes, or jam up. So it is only going up half way, and your gauge only reads half full. So it could have a hole, it could be sticking, or a variety of things. Before you go doing all that, I'd check the ground wire off your unit, since it is working doesn't sound like a ground issue, but they can be tricky. Good luck.

it will be your float in your tank, you have to drop the tank and replace the float.