I did this with a pair of rectangular back-up lights from JCW, simply spliced into the wire to the stock reverse light, and screwed the new reverse lights onto the stock tail-light plastic housing so wiring was short and the new reverse light position threw light from a relatively high position.
It works extremely well, no switches or relays needed and zero wiring or electrical issues. When completed I covered one side to compare stock vs this set-up, and the new lights made a night-and-day difference to the reverse lighting.
Since then I've added corner armor with circular LED taillights, and have all the above if anyone wants to purchase it ? Ready to install quickly by taking out four screws and swapping the stock taillights. It's not the prettiest set-up but does work very well.