From the B737-800 manual:-
If the SPEED BRAKE lever is in the DOWN position during landing or rejected
takeoff, the auto speed brake system operates when these conditions occur:
• main landing gear wheels spin up (more than 60 kts)
• both thrust levers are retarded to IDLE
• reverse thrust levers are positioned for reverse thrust.
So speedbrakes will not deploy until reverse thrust selected. This is surely to back up in case speedbrake is not manually selected?
Also:-
• Simultaneously close the thrust levers and disengage the
autothrottle
• Apply maximum manual braking or verify operation of RTO
autobrakes
• Manually raise the speedbrake lever
• Apply maximum reverse thrust and stop the aircraft.