Which side of the trans light?
Is it the side that is switched by the relay (290/291) OR the side going to pin U (657A)
That is what I asked the OP for originally.
My suspension is it is being back fed from pin U (657A) and seeking ground through 290/291, this would assume the LED is set up so it would not matter which way it was connected as this would be reverse current flow.
If this is correct and all other functions of the TCM work (shifts etc.) a diode could be placed in line with the lamp to extinguish it, as long as what ever has failed and allowed the "backflow" to occur is not causing other parasitic drains on the battery.