Does the tender have two pick-up rollers on its front truck, or a second roller, on the rear truck?
If the tender has two rollers, ("yes" to either of the two situations in the question above) the front pickup roller of the tender (which is energized with "hot" from the middle rail, via the second roller), is shorting across the side of the movable points. The points are energized with the "outside rail" side of the circuit. Try to place a small piece of tape (something that is really sticky) along a short section of that rail. You don't need to run the train to test it. Take all the cars and the loco off the track, leave the tender on the track, and with the track power turned on, slowly roll the tender along the route by hand. You will soon be able to see exactly where to place the tape.
I have tried all kinds of tape in situations like this, and I have found that they all seem either to fall off or wear out after a short while. I finally decided to use a small section of a "peel-n-stick" type mailing label. Some of those have adhesive that really is tough. You can also try gluing a piece of thin plastic with really strong glue.
There is a more scientific way of testing the trouble, using an ohmmeter. You didn't say if you have one handy, so try the above method first.
