Tow bar itself should be easy enough. You may even find ready threaded mounts under the floor but it’s more likely to need holes drilling.
I’d be inclined to try a bar, bike rack and bike first and see if it obscures any lights or the numberplate. If it doesn’t then I’d not bother with the electrics at all. If it covers only the plate then you can get a spare one made for a tenner at most factors(you have to take your V5 in with you nowadays).
If you do need a light board then assuming the car doesn’t have can-bus or some other weird wiring layout (my car needs a relay box despite not being can-bus) you could get a wiring diagram for it and splice the trailer socket wire into the lighting loom in the boot. Just don’t use those bloody blue scotch lock connectors, they’re rubbish. Even choc blocks and tape would be better.