How do I coat the edges of a table top without drip marks?

You don't coat the edges separately. When you pour the flood coat of UltraClear Bar & Table Top Epoxy, it self-levels to 1/8 inch on top and flows over the sides, coating them with the same 1/8-inch layer for a seamless, rounded-over transition from top to edge. There is no special tool or technique for the sides, and even a 2-1/2 inch thick edge will be covered.

The one thing that matters is quantity. Pour enough epoxy to account for roughly 30% of the material running off over the sides. If you only pour enough for the top, the sides will not get covered. Size your batch with the coverage calculator: https://www.bestbartopepoxy.com/pages/epoxy-calculator

Start at one end of the surface and pour in a zig-zag motion from side to side, working your way down the length. Don't spread, trowel, or work the epoxy; it levels itself. Put painter's plastic under the piece to catch the runoff.

If you have already poured and the sides didn't get covered, brush more epoxy onto them. Within 4 to 10 hours of the pour no prep is needed. After 10 hours, wait for the layer to dry, scuff it with 220 to 320 grit, and clean it with acetone before brushing on more.

For an undermount sink cutout, coat the top before the sink is installed, or set up a temporary dam around the opening: https://ultraclear.helpscoutdocs.com/article/223-temporary-dam-epoxy

Tutorial videos: https://www.bestbartopepoxy.com/tutorial-videos/