"In certain Boeing aircraft, with the speedbrake down (i.e. not armed), raising either reverse thrust lever to the interlock stop mechanically moves the speedbrake into the armed position and it will then deploy if the autospeedbrake system is operative and the relevant conditions are satisified (which they should be following an RTO)."
The part of the quote that says "...if the autospeedbrake system is operative..." was a learning point a while back. The autospeedbrakes circuit breaker had been pulled and collared by maintenance due to a fault. We discussed whether the SBs would deploy upon selecting reverse after landing. They did not. We thought we had learned in training that the reverse levers would mechanically deploy the SBs. The way X describes it is the most accurate way of explaining it.