Your tender has a very common and fixable problem.
The reversing mechanism works off solenoid that as power is cycled, the solenoid causes a lever to move a cylindrical drum to switch the power from neutral, forward neutral reverse.
What happens is the drum / ratchet / pawl often sticks and the drum does not rotate. Since you can hear it click, you are getting power to the solenoid.
Take the shell off the tender, holding the tender upright because gravity is part of the motive force doing the cycling action apply power to the front and rear truck metal wheels. Watch the drum. If the drum does not move using an electrically friendly lubricant and while cycling the drum with the lever that sticks out the back of the reverse mechanism spray clean and lube the moving parts. While cycling the drum by hand look at the tiny fingers that should be touching the drum. If they are not touching carefully bend the fingers to touch the drum. If the ends of the fingers are worn off there are replacements.
When you are at the point the drum cycles with each cycling of power and the fingers are making contact re-attach the loco and give it a test run.
Jim
My A/F 4-8-4 made about six laps around my track just fne. I used all functions forward and backwards.
I stoped the train and as tried to start it again it would not go. The tender was clicking as I "pumped" the lever on the tramsformer. No shorts on the track or in the transformer. The problem is in the tender, also I mover the lever under the tender and had no luck. After pumping the lever 15 to 20 times at one point the engine did start to move at a very slow speed for about while the transformer level was on 90. The train moved about 3 feet and I stoped it. The train would not move after that.
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