Trying to solve a lighting problem for a deck. The installation is split into two zones to balance the drops but both are connected to the same Low volt output. No service guide is available. The 300W xfrmr has a high volt and low volt out. I'm assuming they are 12 and 14 volt respectively. The dimmer group or 6 lamps just has a longer run than the other. The wiring supplied by the kit looks to be heavy duty lamp wire, maybe 16 or 14 gauge.
My question is, can I put the dimmer leg on the 14 output and leave the brighter, closer to the source leg on the 12 v output?

Yes, you can give that a try. Increasing voltage helps with voltage drop.

I caution you be sure the transformer output is 12/14 volts. Usually it is 12/24 volts.

24 volts will be too high for the 12 volt lamps.

Best to use a volt meter to measure the actual voltage, even if the nameplate is readable. No guessing allowed with electricity.

What is the make and model of the transformer.

How long are your two runs? Are all 6 lamps dim or do they step down and get dimmer as you get further from the transformer/ What is the wattage of the bulbs for each run; 10w, 20w or what?