Hope this clarifies things as some of the B737NG info and terminology is a bit mixed up!
Auto Speedbrake General;
The auto speedbrake module and the auto speedbrake relays control the automatic operation of the speedbrakes using data from the following sources:-speedbrake arming switch
-speedbrake RTO switch
-Autothrottle microswitch packs
-Antiskid/Autobrake control Unit(ACAU)
-Air/Ground relays(2)
-Antiskid sense relays(2)
-Flight Control Computers(2)
-Radio Altimeters <10 ft relays (2)
LANDING
During landing,the auto speedbrake operates when all these conditions occur;
1 altitude <10ft(signal from FCCs to 10ft R/A relays)
2 The main landing gear is on the ground OR main landing gear wheel speed signals(min 2 <60kts)
3 The speedbrake lever in the armed position
4 BOTH thrust levers at IDLE
During landing,the pilots arm the speedbrake lever.During the flare or at touchdown,the pilots move both thrust levers to idle.Just after touchdown, the auto speedbrake actuator fully extends the speedbrake lever.This commands all spoilers to move up.
The auto speedbrake actuator retracts if either thrust lever is more than the idle position once on the ground.
REFUSED TAKEOFFS (RTO)
During a RTO,when the pilot moves at least one of the thrust reverser levers,the speedbrake refused take off switch closes.This permits the auto speedbrake actuator to extend fully.This commands all spoilers to move up.
The auto speedbrake actuator retracts if either thrust lever is more than the idle position.
MANUAL SPEEDBRAKE CONTROL
When the speedbrake lever is moved up,the speedbrake lever cables move a quadrant in the spoiler ratio changer.The ratio changer moves the spoiler mixer,which supplies an input to the ground spoiler control valve.When the speedbrake lever moves past 31 degrees,the ground spoiler control valve sends hydraulic power to the ground spoiler interlock valve.
A push/pull cable connects the ground spoiler interlock valve to the right hand main landing gear torsion lind.When the airplane is on the ground,this cable opens the ground spoiler interlockvalve.This permits pressure to go to the ground spoiler actuators causing the groung spoilers to move up.