I have never read anything definitive, nor spoken with anyone who was associated with the compnay, in determinimg the transition from the black perimetered "T" to the white. It was, however, a question a friend and I explored during 27 years of accumulation so my response is based purely on personal experience through items owned or observed in other collections. We had come to the conclusion that 1939 was the final year. We saw many examples of the black "T" dated '39 but nothing ever later.I have both a porcelain "Consignee" key hole and "No Smoking", with the black "T", and each are dated 1939. But, to show you no one has "seen it all" nor knows it all, this year produced a "Distributor" keyhole sign ink-stamed by Veribrite-Chicago 7-46. It throws everything I thought I "knew" far off center.
I just got a new computer and do not yet have software to reduce photo file sizes but would be happy to supply pictures sometime soon. Let me know at email@example.com if interested.