TabClose autocmd?

Is there anyway to emulate the function of an autocmd which would trigger on closing of a Tab?

The reason is, I'd like to have a function (maybe a plugin) to track, in order, the most-recently-used (MRU) tabs, and maintaining that history requires reshuffling when a tab is closed. I looked through h: autocmd-events and though TabLeave is promising, ultimately it's insufficient because tabs can be closed without having focus (e.g. :tabonly, or mouse). Various file and buffer triggers/events aren't suitable because files/buffers exist independently of tabs. Any ideas, or is this out of reach?

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