66 block requires the correct
impact punch-down tool, designed to be used with solid telephone wire, no insulation stripping is required. Linked tool usually has both the 66 punch/cutter and the 110 punch/cutter used for a lot of modular wall jacks and cat 5 terminal blocks. Most telephone/data termination is done with 24 gauge wire, some 22 gauge. A 66 block can also be purchased split, (2) terminal on the left are separated from the (2) terminals on the right. There is a bridge clip that can be installed to connect all (4) terminals pictured. A common terminal block has (50) rows of (4), as pictured, to accept a (25 pair) cable. To connect more than (4) wires you have to connect several rows together. Click on the underlined phrase to link.
Usually this tool is more money than most want to spend. From the Ideal website.
Unfortunately some of those very small lighting wires would still be an issue, too small for this termination system, and most likely stranded wire.