Fuses should always be used at the power end to protect the downstream cabling (before the next fuse if any).
Does the switch get hot if the lamp is disconnected (eg - it's ground lead disconnected)?
If not, then it sounds like a hot lamp.
Otherwise it is the current draw (or crap switch). I once had an illuminated paddleswitch rated at 16A for my 8A fan. The switch eventually melted.