Double light switch wiring puzzle

[westward10]

The disconnected reds does one of them come from a cable with a black wire or do they both come from cables with black wires.

 

[westward10]

If the cabinet light works on the switch, the two wires you have connected must be the live power in and the live feed to the cabinet light, but we don't know which is which.
With the power turned OFF, mark those two wires somehow (dots on the wire with permanent marker is a common way), then disconnect all the wires from the switch, and temporarily join all four incoming red wires together. (put them all in any terminal of the switch), and see if both lights come on when the power is temporarily turned back on.
Is there a shaver socket in the bathroom that is not part of the cabinet?

The OP has limited electrical experience so this is a seriously bad idea.

 

[brianmoooore]

I fully agree that the OP has limited electrical knowledge, and considering the fact that this switch seems to have far too many wires for what it does, my normal answer would be to get an electrician in.
Unfortunately, Covid-19 has made this a non starter. I know exactly how they feel, living in a house with my wife, where no one has crossed the threshold for a few days short of a year, and nothing has entered the house without being sterilised or quarantined first.
In this case, we have to balance the dangers of DIY electrical fault finding against the dangers of an elderly gentleman trying to use his bathroom in the dark.

 

[Tony K]

Thank you brianmoooore and westward10. Your advice and suggestions were very much appreciated. The light is now working. My father is delighted and thanks you too.??

 

[brianmoooore]

?

 

[westward10]

Glad it was sorted.