I frequently get the handbrake on warning light when driving.
This is because, when released, the handle will no settle in the 'down/off' position and rides back up slightly.
Is there an easy-ish fix for this?
not heard of that one before... I'm thinking all that can cause that is if the cable is pulling on the handle which can only mean the cable isn't moving freely.
What model do you have? or in other words do you have drum brakes or disc brakes on rear?
its going to be a poorly adjusted handbrake cable
Or a binding point in the rear drums
My advice
Slacken the internal tensioner off
Whip the drums off - remove - clean - copper slip - refit - foot adjust - internal adjust and see if that cures it