'87 used a speedometer cable so either you forgot to hook up the cable on the tranny or forgot to put in the gear.
There is an off-chance the new tranny is missing the worm gear on the output shaft or it has come loose.
Ford fuel gauge gets power from a 5volt pulse power supply behind the dash board, and wouldn't read at all if that was bad, so it is working.
There is 1 wire that runs from gauge to the sending unit in the gas tank, sending unit has a float attached.
The sending unit is the Ground for the gauge, float going up and down changes the OHMS(ground) and the gauge changes.
A volume control or a light dimmer works the same way, as you rotate the **** the OHMS go up or go down, if there is a short inside this part then OHMs can jump high or low.
1987 sender would show 75 ohms Empty and 10ohms Full(in '89 they changed)
It reads like your sender has a short inside, when float drops down enough, below 1/2 then sender ohms jump high, so gauge shows empty.
Could just need a good cleaning.
Good read here on the gauges and senders: Fuel Tank Sending Unit Tech - FORDification.com
'87 2.3l will have a distributor with TFI module and coil, tachometer would usually be hooked to coil's "-" terminal, dark green wire, but could be hooked to TFI module.
Find the coil's "-" and follow that green wire it should go to TFI module on the side of the distributor, there should be a splice, and thats the tach wire.
If you have fuel injection there there will be TWO temp reading devices on the engine.
ECT sensor, 2 wires, only used by the computer.
temp sender, 1 wire, only used for dash board temp gauge
Find the 1 wire sender, turn key on, disconnect that 1 wire from sender.
Gauge should be below COLD now
ground that 1 wire to the engine or battery negative with jumper wire, gauge should now read above HOT.
If this happens gauge and wire are good, replace the sender.
If gauge doesn't move then you will need to get behind dash and start checking wires.