I have not seen a shower like that, with those internals for a long time, I would suggest it is way past it's best.
It looks to have been mounted on top of the tiles, so no re tiling needed, electrics and water feeds are also external, so should be easy to replace with a modern unit. NO! An earth leakage fault is not a trivial fault.
For what a new shower would cost, it is not worth it – I think some people need a reality check before offering advice about repairs. While you may run the risk yourself, encouraging others to do the same is bordering on the criminal.
Sorry to be so forcefull about this, but what you or I may do in similar circumstances is one thing ( that is your and my risk), to encourage others who may not have the same skills or equipment, is another thing entirely.
BUY A NEW SHOWER!