so you have the ECT - and not the fully hydraulic transmission.
The transmission has two main wiring connectors - one large which is the Park Neutral cut out and selector indicator its large and has about 6 or 8 wires. the other would be where the usual OD connector is in the hydraulic transmission - but in your case would have 3 wires instead of just 2, the 3 wires are coming from the ECU going to the shift solenoids inside the transmission.
The ECT button is directly connected to the ECU and not with the transmission. And the symptom/action you are talking about is very very normal - the transmission will not engage OD unless the engine is hot. If it was not operating correctly before it is now
The ECT will delay upshifts causing the transmission to hold its gears longer, going to Normal mode the tranny will quickly upshift causing the rpms to fall and cruise. All this is also affected by position of the Throttle Position Sensor also - The TPS is what dictates kickdown in your transmission - not the cable like you would naturally assume