B737-700 Captain reported communications issues and MEL compliance issues complicated a maintenance delay and contributed to down line complications with the MEL procedures.

Narrative

First flight of the day. Walking down a jet way; I saw a Captain of inbound flight was on a phone; talking to Maintenance. They explained: Speed Brake Extended Light came on during taxiing to the gate. They had reset the Speed Brake Handle few times; but the Light would come back on every time. So; they called Maintenance and the Station Maintenance. I have checked the MEL and learned that such malfunction may or may not be deferred; depending on location of the fault. I have decided to delay boarding. The Station Maintenance Mechanics did go through their procedure checklist and came to the conclusion that the Speed Brake System operates normally and the Fault is in a monitoring System. So; the Fault in a Monitoring System was deferrable and they start their paper work. I have checked the specific MEL and called Maintenance in ZZZ1. Maintenance Control confirmed that we are good to go; but in case the Speed Brake Extended Light will continue causing a problem; they will ask me in ZZZ2 to remove the Respective Light Bulbs. During taxi out; the Light came on; I had reset the Speed Brake Handle; but Light would come back on few seconds later. During pre-takeoff check the Takeoff Configuration Horn came on. We have checked the takeoff configuration and everything was good. The cause of the horn was well known and I proposed to continue. The takeoff configuration horn sounded during takeoff roll and silenced right at airborne. The rest of the flight was uneventful. I have called to Maintenance after landing in ZZZ2 and have removed Light Bulbs from the Speed Brakes Extended Light as I was directed. It was no issue anymore and we successfully completed two more legs on this aircraft and passed all the information to the next crew.