Thanks, C. W.
OK, I pulled the shell off and saw no obvious problems. I hooked it up so that I could observe the innards in action (and, yes, I was VERY careful to avoid touching anything inside while it was powered and operating).
When I pulled the lever to trip an E-unit, a puff of smoke came from the reversing switch. I don't mind smoking trains, but I dislike the thought of a smoking transformer!
Any recommendations from anyone?