Is there a brand of clear type liquid sealer I can use on rocks?

I would use clear caulking or mod podge gel medium.

I would use an 2-part epoxy called bar top pour.... https://www.youtube.com/watch?v=CsVLhk55pWM

Try an epoxy or bar top kit- just make sure you block off the edges.

To get a firm but temporary edge:

Glue wax paper to 1 side of balsa strips (your local craft store), precut to the lengths you need. Try to have a 1" overhang of paper on all sides.

Using a staple gun, attach each strip along the outside edge of your surface. You will want staples long enough to go through the balsa & about 1/8 to 1/4 inch into your vanity. You will need 1 staple on each end and 1-3 in between. Make certain that your wax paper is on the inside. For the corners, use a regular office stapler to staple the overhang of one strip to the next.

Once your epoxy has set, tear away your balsa. You used the softest wood on Earth so you could do this. Some may cling under the staples, don't panic. Using an office staple remover, push out any remaining balsa & pull out your staples.

Remember the overhang of max paper on all sides? Tear off bits from the broken balsa and wad them into ball-like smooshes. Use the waxpaper to buff into the holes. Your holes should be all but invisible even under scrutiny.