Battery light circuit is very simple, almost the samething as temp circuit
Battery light bulb gets 12volts from Cab fuse 15 with key on
Bulbs ground is the light green/red wire on the alternator's 3 wire plug in
When an alternator is not spinning its at 0volts so "like a ground", so bulb has 12v and 0v and it lights up
When alternator is spinning its generating voltage, lets say 14volts
So now Cab Fuse 15 is 14volts and Alternator's light green wire is 14volts, no ground(0v) so bulb is off
Key on(12v)---Fuse 15-----battery light bulb---------------alternator
If alternator was not working or generating less that 12volts(battery volts) then battery light would come on or stay on
Fuse is OK since Battery Light is on with key on
Unplug the 3 wire connector on alternator and Battery Light should go off
If not then there is a short to ground somewhere, in the cluster or on the light green wire
But its beginning to look like a cluster issue
On the back of the cluster is a separate module for the gas gauge, the anti-slosh module
This is used to prevent gas gauge from going up and down every time you go around a corner and the gas in the tank "sloshes around"
And they do fail, but............float in the tank can also fail, fills with gas and sinks to the bottom
If you pull out the cluster to check wires, you can test the fuel sender wire, yellow/white wire pin 12 on 12 pin connector
Sender uses
16 ohms Empty
158 ohms Full
So you should see between 16 and 158 ohms and if you rock the truck the fuel in the tank will slosh around and ohms will go up and down, if so float and wire are OK, so anti-slosh module or cluster is bad
If 14 - 20 ohms then float may be bad, sunk to bottom(assuming tanks not Empty, lol)
If lower than 10 ohms could be a short in the wire or sender
1996 thru 2003 Ranger or Mazda B-series Clusters are interchangeable, plug and play, with or without Tachometers, all Rangers/B-series are wire for Tachs even if they didn't come with one