Short one, and mainly for my own reference.
I’d installed PHP 7.0. Updated the nginx config files to use php7.0-fpm.sock. Changed the PHP user. Everything *looked* like it should work, but I was eating gateway errors.
Turns out the default “listen” path had slightly changed in PHP 7.0 (/run/php/php7.0-fpm.sock instead of /var/run) and I’d missed it, so all my nginx entries were now pointing to a non-existent path to the socket. Rather than go through nginx and change them all yet again, the easy method is to just edit /etc/php/7.0/fpm/pool.d/www.conf and change the listen path there.