Actually now I'm no longer in the middle of a sword trial (just got absolutely mullered by a god damn Lionel) I realised I could test it by fucking about with the joy-cons removed from the tablet. It is indeed the right one.
I think my issue is a temperamental connection with at least one of the joy-con rails on the tablet, might have to try pushing them out, maybe add support behind them? I'm sure I saw a helpful comment from someone years ago who did this, apparently I didn't bookmark it.
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Fuck a duck, it happens with Bluetooth connection too. Apparently the gyro in my right joy-con only works some of the time, and this is unrelated to the rail connection issues I have with the left joy-con.