How does your company test mechanical jumpers, specifically the insulated cable/wire? Does the cable/wire have to be submersed in a test tank or is a visual inspection of the insulation acceptable? Are mechanical jumpers considered live-line tools under 1910.269(j)? I'd appreciate your responses!

A live line tool is a hot stick.

Not sure exactly what you mean by jumpers. If you mean for instance personal grounding sets the standard says that you inspect visually before use. Actual testing is only done if repairs or modifications are made. We're a mine so we use a lot of trailing cable (SHD-GC) which requires a visual inspection and an insulation resistance test before putting it in service every time but that's all. If it's intended as portable cable that's what you'd do anyways. You can't for instance use MV-105 for portable cable because it's not rated for that service. In fact outside of low voltage I'm not even sure under UL there are ANY portable cables and thus voltage stress is simply not a factor. Portable power cables for medium voltage fall under NEMA/ICEA specifications and are tested and Listed via CSA for use in the US in an OSHA jurisdiction. Since UL doesn't maintain the standard, they won't register anything with it either. They're funny that way.