Welcome to TRS
From your description, the starter relay is not getting the 12volts, on the "S" post, from the ignition switch, this 12volts activates the starter relay
"S" post is the smaller post on the relay with the red/blue stripe wire
In a 1990 Ranger with automatic trans, the red/blue wire comes from the NSS(neutral safety switch) located above the shift rod on the drivers side of transmission
There is a 4 or 5 wire connector on the NSS
2 or 3 wires(all red/blue, but one may be Pink) these wires are only connected together when transmission is in Park or Neutral, this prevents "starting in gear", so this switch passes the 12v from ignition switch to starter relay "S" post, but only when switch is in the correct position
NSS is a plunger type switch
NSS also has 2 wires for Reverse Lights, these 2 wires are connected together when trans is in Reverse, and then backup/reverse lights should come on
The red/blue wire from ignition switch is actually PINK at the ignition switch, it changes from Pink to red/blue at a connector above brake pedal under dash, this is where a Clutch Pedal Switch would be on a Manual trans Ranger
On some Rangers the Pink wire will stay Pink all the way to NSS
So you have
Ignition switch--(pink wire)---connector under dash----(red/blue or pink)----NSS----(red/blue)----(S post)Starter relay