Hello Tom,
I fitted a quick shift gear link to mine and seem to remember this plastic yellow thing, I think mine was just about snapped off, the new gear linkage hasn't got it either, I believe it serves no purpose.

If by fiddling with the ESP button you managed to switch it off I would say the switch is the problem, but DO CLEAN the connections under the switch first, they may be dirty.

It probably would be cheaper in the long run to buy a fault code reader and do it yourself. The Management light comes on now and again in my car especially if I stall it So I just reset it with my Bluefin.
It can come on if you get a loose loom plug connection for example and as I said above mine comes on if I stall ahem....
You don't want to be paying a Garage to reset the Light for something that you can do yourself.
Oh yeah, also after the light comes on, in some cases if the fault doesn't happen again for a while, the light goes out anyway, but not all cases.

Hope this helps
Cheers