There's a coolant temp switch in the o/d relay coil ground path that won't let it go into o/d until it warms up. If your thermostat is bad (stuck open) or missing it will do what you describe. You can ground the wire at the sensor/switch, replace the t'stat, or replace the sensor/switch (on the water neck, one skinny wire connection. Other one wire sensor is for the gauge. Two wire sensor is for ecu.

Not responsible for advice not taken...