Well, Yor, I can see why you've had so much trouble locating what happened to WHBjr. I've looked everywhere I can think of & can't find a clear mention of him after 1871 either.
This got me to thinking: maybe there's a more simple explanation..? Taking into account that he wasn't mentioned in his Dad's 1882 will, and no clues for him outside of England after 1871, I took a closer look at the England death registers for something between 1871-1882.
Obviously there's nothing there for Brusey, but I did find this:
England & Wales, FreeBMD Death Index: 1837-1915
Name: Male
Estimated birth year: abt 1849
Year of Registration: 1877
Quarter of Registration: Jan-Feb-Mar
Age at Death: 28
District: Caistor
County: Lincolnshire
Volume: 7a
Page: 426
On one hand, it's a bit of a long shot, right? But on the other hand, if it's not WHBjr, then it's quite a coincidence that there was a 2nd male, at WHBjr's age, whose death was within the same logical timeframe, in the same area where WHBjr lived & where WHBjr's relatives died, who wasn't properly accounted for.
Speaking of coincidences, my own Gx4-Grandfather's story was a similar mystery for me: I couldn't find his death anywhere either after seeing him last in an early census. Until of course I took a similar look at the death indexes, and found a man with all the right details except the surname. Took a punt and ordered the death certificate, and turns out it was him, with the correct surname. There had simply been a mistake in the index, on the actual page, where he'd been grouped with others with an "alphabetically-nearby" surname.
So have you seen this lead yet & ruled it out?