Safe repair for electric shower casing
What jurisdiction is this located in?
In most places in the US it is illegal for a non-licensed person to do electrical work in a rental.  Technically even buying a part for this device and replacing it would be a violation and absolutely repairing the circuit board in it would be a repair and thus illegal if you tried doing it.
And if your idea is you are going to call an electrician to come in and repair this and start telling him or her how to do their job they are going to turn and leave.  Many probably wouldn't touch this one in any case as it is due to the missing tiling.
Since your landlady is paying for it you have no vested interest in the amount of money it would cost.  The people who would care about that are the ones who are intending to make some money on the side by getting a quote then doing the work themselves (illegal in the US) and then passing the quote to the landlord.
The landlord has huge liability here for a tenant to get involved in this kind of repair.  What happens if you contract with an electrician to do this, then 6 months from now a future tenant gets electrocuted in the shower and they go back to this electrician and he claims that he never touched it?
In the US the landlord is legally required to provide a safe rental with everything working.  Your landlord has already broken the law by allowing you to rent this place that a &quot;prior tenant broke this&quot;  Because of that you can legally walk away from the lease (she has already broken it)