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Thameslink RPI's are allowed to work solo but if availability is there then they will work together in teams. With southern, teams generally go out in 2's or 3's but on long trains or 2 coupled units (eg 455's) then you can get separated but will try and meet up with colleague at earliest...
As someone who works as an RPI in the south london area, i will ask to see railcards 100% of the time and unless a pretty miraculous reason is given for not carrying it then the minimum issued will be a penalty fare.
Follow the advice, keep it somewhere where you're less likely to forget it