Judging by the lack of replies I'm going to guess this just isn't a thing. Bummer.
For anyone interested I've found a solution, of sorts. If you have an android phone or tablet there is an app called DashmeterPro that has a version compatible with F1 2016 and will display very clearly your current gear (among other things).
Admittedly, it's not an ideal solution as it requires launching the DashmeterPro software every time you wish to play F1 2016. Also having to plug in your phone/tablet (so the screen doesn't turn off) and find a suitable spot to place it so it's visible in-game every time is a chore as well, but it's better than nothing I suppose. It is a very nice app, and if you play often I could easily see how it might be worth it to invest in a cheap android tablet and stand to dedicate to it.
For anyone interested. there are several versions of DashmeterPro on the Google Play store, the one that works with F1 2016 is (oddly) the Richard Burns Rally version. The instructions were somewhat confusing (for me at least) as there is also another piece of software that must be downloaded as well from the developer's website so if anyone needs assistance just ask.