The rectifier's condition would have no effect on reversing.
Based upon your description, I would guess that the reversing / whistle switch is in need of some attention.
The switch assembly probably needs a good cleaning, and the little retainer (looks like a top hat) may have slipped, or completely fallen off.
The odor might just be dirt, or old lubricant on the switch surfaces. IMHO, those surfaces should not be lubricated, but some people do. The old lub could be causing the smell, and affecting the operation.
