Yes the tail lights come on and yes they're dual filament. Intact, not burnt.

 

That is just the taillight lense, that would not be the part.

Right side would be Honda Part Number: 37540-SM4-A01. It is the little box like in the previous images I posted.



Edit: My mistake, your PM said right side (passenger side).

 

Here is a test if you want to try. Verify the wire colors first.

Unplug the 8-gray connector (connector C715) shown in the attached image. With a wire or small paper clip, jump the 8P connector female terminal cavity (where the Grn/Wht wire is) to the female terminal cavity (with the Grn/Yel wire). The Grn/Wht wire is a wire with green insulation and a white stripe running through it. Depress the brake pedal; does the high mount brake light work?

You can then jump the Grn/Wht wire female terminal cavity to the Grn/Red wire female terminal cavity. Then depress the brake pedal, does the right inner brake light work?

If they work this way, you probably have a faulty brake light failure sensor.

 

Hey guys! Read this thread. The OP just said that all this is crap - a non-problem - because the tail-lights do in fact come on.

*****
To the OP, don't take your car back to that shop.
Your local Honda dealer is the best normal solution to false mechanical claims.

 

UhOh, the OP does have an issue/problem, it is with the brake lights. It probably is due to the brake light failure sensor. The bulbs are dual filament; one filament is for the brake light when the brake pedal is depressed; and the other filament is for the taillight when headlights or parking lights are turned on. The electrical circuits for the two are separate.

She had previously contacted me via PM to state an issue with the "right brake light".