While I know of nothing in the Law prohibiting it, as a matter of protocol I would only wear the T2K apron in another Lodge if I was there to promote T2K or on some other sort of official business regarding T2K.
Brother Cook:I think you mean Jeremy Cross’ first monitor, as Webb (and in a practical sense, Pritchard) monitors were before that.
For additional history, see http://www.themasonictrowel.com/Articles/Symbolism/general_files/past_master_jewel.htm
This magnificent jewel was presented on April 12, 1831, to Worshipful Master William Cuscaden by Benevolent Lodge No. 142, New York. It is made of gold, silver and composite metal, with inlaid rhinestones and an amethyst, and with what may be a ruby at the top. Brother Cuscaden was first seen on...nymasons.org
Not all jurisdictions mandate a form of PM jewel.
PM jewels within jurisdictions vary. https://masonicmedals.net/product-category/medals-jewels/past-masters-jewels-th453-th455/