@Chris S I still don't think you have told us what the lights are for?
For night time riding in the country or just "to be seen" lights in town/built up areas.
May then be able to give some relevant advice.
The good news is that you don't need to pay a lot for perfectly decent lights these days.
That will stay on over bumps.
Nor do they have to be "dogs bollocks", "bad boys", "bitches", "laser eye burners" or whatever. Or incredibly i
ncredibly incredibly small.**
If you ride in London (haven't checked) please don't be one of the nits blinding me for no good reason at all.
I'd second advice above to always use two rear lights - and mount them sensibly - and ensure that aren't or can become obscured.
** though for folks who demand such performance from their city lights I can assure them that I am still working on my prototype suppository that will make their arse flash like a giant distress beacon. It will be sold on a monthly rental basis with a course of dietary supplements which will ensure that their rear flesh continues to shine and pulse to the max, whatever the ambient temperature. By internalising the light they will of course add not a microgram to the bike's weight.