11 seconds seems a long time to not initiate manual braking. I fly a 737 classic into shorter runways than that and whilst using autobrake I will almost always 'follow through' on the brakes manually and if it doesn't seem enough then my pressure will trip out the autobrakes and give more manual braking. I wouldn't necessarily notice if the spoilers didn't deploy - its the nhp's job to monitor that.
There would be a large stagger between the thrust levers on a 737 which would be very noticable if you didn't close one - and don't forget reverse is a different lever attached to the top of the forward thrust lever, so even with one locked out the levers will both be in the same position at idle, but one will have the reverser lever up, one won't - it would be wire tied.
Also, in some airlines that fly monitored approaches the Non handling pilot selects reverse whilst the handling pilot initiates / monitors braking.