Welcome to TRS
Google: ford ranger door ajar light stays on
It is a common issue and often can be fixed by spraying WD40 or similar into the effected door's latch mechanism
Yes, it could be a wiring problem, but...............some sellers do disable lights on purpose so things "look fine" when they are not, so just a grain of salt.
CEL(check engine light) should come on when you turn on the key, shows that computer is booting up, then it will go off after engine starts up, assuming there are no codes set in computers memory, if there are it will come back on.
Most buyers would shy away from a vehicle with CEL on all the time, so...........bulb is pulled out or blacked out with tape.
Most warning lights in the cluster, including the CEL, get 12volts when key is turned on, the way they are activated(light up) is by GROUNDING the bulb.
You will need to pull out the cluster and check voltages and GROUNDS so have a volt/ohm meter to do this testing.
Also test the bulbs and have some extras handy
You may want to change all the cluster back light bulbs as well, 6 of them, not expensive and hard to get to, so just do it now, they are 17 years old.
I posted wiring diagram for 2000 Ranger instrument cluster in this thread that you can download and print:
http://www.therangerstation.com/forums/showthread.php?t=167158
CEL is called MIL by FORD in the diagram, MIL = multi-function indicator lamp, because it also will come on if there is a transmission problem(automatic), or emissions problem so not just "engine" issues