Quote from Andreas Grauel :

cause some people has problems with the pitlimiter and have to push it twice or something to get it on/off !
I dont have this problem but heard about it very often

I have noticed this behaviour as well but, for some reason, it especially often occurs on Westhill track and rarely on Aston track (with FZR).
I am not using any key assignment script, only the in-game built-in settings.

It has nothing to do with my wheel because the same behaviour occurs even when using the default keyboard L key. And even if the car is parked on the track / stopped inside pit box.