The two feeds would work in parallel, and as a result the bulbs would only receive 12-volts. And the bulbs will use the same amount of current as they would with a single feed, no danger of them using more current and potentially being "too bright".
I have a 2014 Explorer which uses LED tail and brake lights also, and wired them for towing with Roadmaster diodes. No problems at all in the two+ years I have drug it around. And there are times the lights are being fed from both systems without issue.
2014 Seneca 37TS
Toads: 2014 Ford Explorer Sport or 2013 Ford Focus ST