See this sentence "This is my last night working here"! What grammar structure is it? Reduced Relative Clause?
Solution 1:
There are two elements in the gerund-participial which are understood through context:
(subject) working here (temporal location)
The subject of working is inferred from my.
The temporal location is interpreted through the head noun night, which in this case could not possibly be the subject of working, and so is understood as the temporal location of the situation expressed by working here.
A similar example with a wh-relative clause where an adjunct of temporal location has been relativized would be:
I would like to say a word or two on the subject of this Amendment before we pass from it, as this is the last night when we shall discuss the King's Speech (Mr. William Watson, House of Commons, 1937)
Which could be paraphrased as:
our last night discussing the King's Speech
Though this version would make it seem that the discussion takes up most of the evening, whereas the original simply locates the discussion (however brief) on that evening.
Gerund-participials as post-head modifier in NPs are very similar to relative clauses, but are not analyzed as relative clauses because it is not possible for them to include a relative phrase. (The Cambridge Grammar of the English Language p1265)
*our last night when discussing the kings speech
Other instances requiring a similar interpretation:
When faced with challenges, Donaldson is fond of telling people that on his first day working at the State Department in 1973 as undersecretary for energy policy, war broke out in the Middle East. (Bush picks polar opposite of Pitt to take over at SEC, Greg Farrell, USA Today 2002)
She'd snuck those shoes out of her mother's closet moments after May Jones left for her PTA meeting, and prayed the whole hour and a half while her mother was gone that she would hurry back and be so dead tired from her long day teaching third grade and arguing with the parents of Spruce Street Elementary School that she'd go straight to sleep without making a big fuss over what time Deena turned the lights out, and wouldn't come back in the house looking for those shoes. (Dreamgirls; Millner, Denene; Harper Collins 2006)
The title, " Ms. Bixby's Last Day, " refers to her last day teaching at the school and the inevitability of one's last day living. (Book review: 'Mrs. Bixby's Last Day' a tale of life, loss for classmates, Virginian-Pilot 2019)
It was like watching a parade of past Julias: a kittenish little number she'd worn during her year singing a cappella; a pleated skirt and sweater set that had been her daily uniform as a temp. (Julia and Sunny, Sarah Shun-lien Bynum, Ploughshares 2018)
His years working in France as a cook had left him with culinary skills far greater than one would suspect from the three-table restaurant he ran with his guest room. (Each Generation Offers Its Kindness; Robert M. Press; Christian Science Monitor 1992)