Captain reported an in flight shut down and diversion caused by a reverser unlocked light illuminating. The Flight Crew elected to divert and make a precautionary landing.

Narrative

My first officer and I were in the cruise segment of our flight at FL360 southbound from ZZZ heading towards ZZZ1 when we received the indication/annunciator that the right thrust reverser had unlocked and the light indication illuminated. I immediately began to slow the aircraft and asked the First Officer to get us a lower altitude. We were handed off to ZZZ1 Center who assigned us FL240. I used the air brakes to help slow us while maintaining a good rate of decent. Both thrust levers at idle. I instructed the FO (First Officer) to run the unlocked TR (Thrust Reverser) in flight checklist. ATC advised us that ZZZ2 was approximately 50 miles away from our position and we asked for vectors there. The checklist instructed us to shut down the affected engine. I delayed doing this until we were lower. In hindsight I don't think it would have made any difference to just shut it down at the time of reading. The TR never deployed and the light began intermittently going on and off. Around 18;000 feet we shut down the right side or Number 2 engine as per the checklist. Advised ATC of fuel and SOB (Souls on Board) and they asked if we needed emergency services. I can't remember if we asked for it or not but they were waiting for us when we landed. We discussed and agreed that we would land Flaps 25 and upon touchdown my FO would select Flaps 45 upon touchdown to insure we could use Lift Dump/aerodynamic breaking; we were single engine with a 20 plus knot gusting crosswind being that we had a great deal of runway we agreed that this was the best configuration for our aircraft. The conditions were less than ideal but I wanted to get the aircraft on the ground as soon as possible and as safely as we could. In hindsight; if I were to change any of my action the only other thing I would have done differently is check the winds at the destination; next time to make sure they are at least down the runway. I felt it was urgent to get down as quickly as possible in case the actual reverser were to deploy.