See small red arrow..
This is taken from left (n/s/f) wing looking down at throttle elbow. I believe it is perhaps related to Pressure Control Valve (PCV) but please educate me. I'm on day 3 of chasing vac leak contributions to a P0171 Left Bank Lean on my 2003 XKR. With repeated smoke tests I found that the throttle body to brake servo boost was leaking, replaced o-ring, didn't fully fix it, and had to resort to RTV around the union. Code came back, and I got a strong positive reaction on Short Term Fuel Trim Bank 1 (STFT) when I hit that end of the tube at the union with brake cleaner. I wasn't able to remove the tube easily, so I felt around the unseen side carefully but couldn't feel any perish. It feels like there is a strong and approx 20mm spigot coming out of the elbow that this tube is firmly on (no clamp/clip). So I'm not sure of the likely failure mode that I'm trying to fix here... at the time I thought potentially corrosion on the under side of the elbow/spigot union.. and hit it with RTV as best as I could. Left it to cure and will try the test again tomorrow and hope not to see the trim move. If this is not the cause, I have an anxious feeling that the next move would be supercharger off and have a kit of all possible hose types and connectors for whatever labyrinth of breathers awaits under there?

 

Ref: part-load-breather-pipe
I had a P0171 issue that thought I fixed around 2015, then in 2019 it returned. The above link tells what i did and what happened. This 2019 hack lasted me until this past February when, while I had the supercharger removed, I did a proper repair with a new part load breather pipe (pt # A84879).
I am not saying that this is your P0171 problem, but even an extremely small leak in this circuit can set off this code.

 

Thanks Dr D, I've written a reply to you 3 times and then clicked away for something else only to find everything I wrote has gone! Bloody annoying... Anyway a big thank you for that part number. Before you kindly posted that I spent a whole day hunting for that pipe's part number and everything that was supposedly correct didn't look like the one fitted on my car. I ordered one that 'looked right' and predictably it was not... but in the mean time I fixed the original's various leaks with RTV and got it to a point where it would pass my vacuum tests on it even when I bent and vibrated it so fingers crossed it will at least allow diagnostics to move on. I've fixed or improved 6 sources of increased air and have just disconnected the battery to see what the trims do next, so wish me luck. But in the meantime thanks to you I'll be able to replace that pipe with the right item (although I'm sorely tempted to replace all the plastic ducting rubbish with decent hose if I can work out the norma connectors business). Thanks again!