It is extremely important! Proper gear lube AND break-in is much more critical on a high pinion differential because the gears are NOT submerged in oil like a low pinion would be.
Fill it to the fill plug that is not drilled/reamed out. One of the plugs is made un-useable so you do not use the wrong plug. Different housing designs allow for different amounts of fluid. More fluid always helps cool better.
Best choice (non-racing): https://www.currieenterprises.com/why-run-conventional-gear-oil
Alternate option: GL-5 rated 85w-140 standard (non-synthetic) gear lube.
For rear applications in desert racing use 2 ½ to 3 gallons of Swepco 203 moly- 250 weight available from SWEPCOUSA.com.