EEC Relay is stuck closed, most likely.
In a '91 Ranger there are 3 relays under the power box in the engine compartment.
Unbolt the Power Box and lift it up, you will see 3 relays
Green base is Fuel Pump relay
Brown base is EEC relay
Black base is WOT(wide open throttle) relay.
EEC relay, when closed, powers the EEC(computer,PCM), the fuel injectors, and the spark system, so basically the engine
This power comes from fuse #8(30amp) in the power box I think, pull that fuse and engine will shut off.
EEC relay closes when key is turned on, then opens when key is turned off.
So either the relay is stuck closed or there is a short in the wiring giving it 12volts all the time, either way getting to it for testing would be the first step.
I believe all 3 relays are the same part number, so can be swapped for testing.
Google: 1991 ranger EEC Relay location
There are some pictures of where the relays are