It was more than obvious that the glow igniter was broken (fractured coil) and it was hoped that it was the sole problem with the range. I initially sourced the igniter from another seller that described the part as "genuine replacement part" and "Whirlpool item", but never had "Whirlpool" and "Genuine" together. The part pictured appeared correct, but with a price too good to be true. The part arrived in a plan brown box, and while the contents were generally the same (e.g. hardware), the coil was slightly different (stretched at the beginning loops.) The part immediately blew after installation. I suspect either the coil was made of inferior material or had a fracture in it.
I went on the search for a genuine Whirlpool part, and here is where I found it. It at least says so on the box I received and the coils were much more similar to the OE part (which has been updated by Whirlpool, so the original is not available.) I installed the new part from AppliancePartsPros, and our problem was solved. The oven and broil light as they should.