Is the trolley supposed to stop over top (i.e. blocking) the sensor or is it supposed to pass all the way over and then stop?

You can also try this as a 4-6-0 starts running at about 4V.
Take a fresh 9V battery (yes, like the ones in smoke alarms)
Take wires off the power pack and connect to battery.
An alkaline 9V has about 550 mAH capacity and should run your loco for about 20 minutes, give or take.
This allows you to show its not the 4-6-0.

Of course, if you have multimeter, monitor voltage on the track to see if power pack is cutting out on overload.

I wonder if your 1400 is underpowered and you are tripping out the thermal protection, that then resets when it cools.
Your pack if 0-14V capable of 13VA (this includes any accessories)
My experience with measuring 4-6-0's is that they require 0.7 to 0.8A while your pack's max output at 14V is 0.9A (maybe as specs are loosy-goosy).
Might need a more powerful pack.

To further confirm, just replaced cracked axle tubes on my Christmas 4-6-0 (v5 chassis) and the new axle tubes with outer metal sleeve from Bachmann worked perfectly (had to use padded C-clamp to fully seat and get correct gauge).
Old wheels had started to walk out of cracked tube, increasing gauge and getting rail rub (squeaking)

My experience is that there are two versions of the standard knuckle coupler (actually there's newer Spectrum version but we're not going there).
The old version has a plastic drop pin that can hangup and work its way upward resulting in uncoupling.
Some suggest a drop of plastic safe lube.
At some point (say around 2000) Bachmann switched to a metal drop pin that is heavier and smoother.
Switched all my couplers to metal drop pin version and have had no issues, indoor and flat.
Pull consist of 10-12 and no problems.
Plastic is easily identifiable as have a hole (i.e. for pull chain) in the top of drop pin.

To keep track together, rubber bands, one on each side connecting the ties.
Would be better to have track on hardwood/vinyl floor or sheet of plywood/mdf over carpet.
Works OK on Berber carpet (short loop).

Description is misleading, they are plastic tubes with outer metal support (to prevent cracking), so they won't short.

Couple choices:
(1) Wrap the cracked plastic axle/spacer with heat shrink tubing.  It holds the plastic in place essentially acting like a girdle.
(2) Replace the plastic axle (if pieces are missing) with a stiff tubing.  Visit you local hardware/plumbing store and experiment with
all the various tubing that exists. Take the wheels with you and find one with an inside diameter (ID) that is a snug fit and then trim to length.
(3) Buy new "Axle Tubes" at Bachmann Parts
https://estore.bachmanntrains.com/index.php?main_page=product_info&cPath=69_623&products_id=11238

As to the tender light, if there are two pairs of wires (i.e. two 2-pin connectors) between loco and tender, then yes tender light should illuminate in reverse.
If only one pair of wires/connector (chuff sound), then no tender light.

Take no offense, but have to ask the obvious: Did you turn on smoke switch under boiler door on front of loco?

Sample image here:
https://estore.bachmanntrains.com/index.php?main_page=product_info&cPath=69_629&products_id=9952

https://estore.bachmanntrains.com/index.php?main_page=index&cPath=69

What is a decent sound card for this Shay?
Keeping it simple, analog control with track power (no DCC, no radio-controlled)
Drop in 3" speaker in tender along with sound card and hook up chuff trigger.
Looking for recent design available from mfgr, not old design that would have to buy on eBay, etc.

Anyone ever found a PDF of the Owners Manual for the 36 ton Two-Truck Shay?

Well I just picked up one on eBay from a estate liquidator for $350 plus shipping.
Came in original Bachmann shipping box with foam inserts.
Date code was C70731 on outer box which translates to 07/31/1997 so this would be first batch??
The trucks were plastic with 8 screws.
Loco was still in plastic bag with about 6 dried out desiccants.
Stack was still wrapped in plastic and accessories were unopened.
Interesting enough the outer box had shipping label from Bachmann to Star Hobby in Annapolis (about 20 miles from where I live)
Then had shipping label from Star Hobby to a buyer.
Then there was label from Allied Moving, seems like my loco spent a lot of time travelling and no time on the tracks.
Need to oil and grease before running.

Before 26 years of aging that all but guarantees that the plastic motor/trucks have disintegrated and will require a $250 replacement with die-cast motor/trucks.