Start Condition:

We are in a reference frame where the Plate is at rest.

Battery is moving to right at .866c and length contracted by 50%

Right Terminal Starts Contact:

Time at Right Battery Terminal = .269 sec

Time at Left Battery Terminal = .358 sec

Left Terminal Starts Contact:

Time at Right Battery Terminal = .307 sec

Time at Left Battery Terminal = .423 sec

Right Terminal Ends Contact:

Time at Right Battery Terminal = .348 sec

Time at Left Battery Terminal = .464 sec

Left Terminal Ends Contact:

Time at Right Battery Terminal = .386 sec

Time at Left Battery Terminal = .501 sec

This is an issue of relativity of simultaneity.

From the point of view of the Plate:

The right terminal is in contact with the plate between .269sec and .348sec. on the Right Terminal’s Clock.

The left terminal is in contact with the plate between .423sec and .501sec on the Left Terminal’s Clock.

The two sets of time never overlap so the circuit never closes, even from the reference frame of the Plate.