Ok- Im not an electrician, but I did stay at a Holiday Inn last night, lol.
I would suggest ditching line voltage lights that are in such a state of disrepair so close to the pool ESP without a functional GFCI breaker. That would make me nervous. But that’s just me.
I bought direct burial 12 ga to run along the side of my retaining wall and on other side of pool deck. I don’t think you need to put a LV connection in a Jbox. I have seen waterproof wire nuts used for custom installs that don’t use the spring loaded connector on the end of box store grade LV fixtures.
That , I think would eliminate the need to run LV and line voltage in the same conduit- which is not typically allowed by code.
My first thought is to ditch the buried conduit around the pool , but it sounds like you need it to supply the pool light and a convenience receptacle.
Your pool pump should be unaffected by all this. If you have a dedicated 15 amp circuit, put in a new GFCI breaker, wire in a recepticle where you want to add a LV transformer and look up volt lighting for really really nice fixtures. Run 12 ga LV to where you want the lights.
This should leave your pool light and convenience outlet protected as required as well as the LV LED lights.
I think the max run is generally about 100 ft for 12 ga. It depends on the number of fixtures, wattage, etc. I found some better transformers have a 15v tap to offset the length of run.
Here is a spreadsheet I found for calculating wattage of transformer.
http://www.wplawinc.com/LiteratureRetrieve.aspx?ID=60726
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