If a prox sensor is giving you trouble, that is false info being fed to the ovhd indication and likely other systems.If the slats / flaps are being sensed as being in a position other than it should be in a landing config, I suspect the speed tape thinks yours slats/flaps are incorrectly positioned as would the
landing config logic hence the warning ie throttles back gear not down or flaps incorrectly set.
Take off warning should be an intermittant horn/tone , landing config I think is a continuous horn/tone. Its been a while sorry it is from memory.
Of course you could actually have a real slat problem but suspect you would know about that!
The previous poster maybe correct some of the LE devices MEL's do/did require removal of lamps on some 737 series aircraft.Not sure about NG.It has a lot less problems than the 737-300/400 series for LE indication issues.