So I asked Tesla to activate Trailer Mode in my gateway config as I bought all the electrical parts from them. Of course they said no, and their reason was there is no option in my car config to do so.
I didn't believe them as the person I spoke to didn't know what Toolbox was. So I decided to buy a service cable (£30 from Amazon), and a 1-hour subscription of Toolbox 3 (£40 from Tesla), to check for myself. I won't go into too much detail in the thread, but of the visible configuration items, a handful of them were unlocked for editing (I'm assuming the consumer version is restricted). One of the unlocked items was for Trailer Mode. I switched it to the only other setting apart from 'none', sent it to the car, and...
View attachment 962555
View attachment 962556
...hey presto!
It cost me roughly £450 to source the parts, fit it myself and activate Trailer Mode.
Happy to answer questions about Toolbox in DM's.