Loop the hockey tape around the top handle of the clipper until it is just big enough that it barely fits in the hollow metal tube. Put the clippers inside the tube and test clamping it with the pipe clamp. Tightening the pipe clamp should hold the clippers in place and the tube onto the metal rod.

This system lets the tube rotate and slide about the rod, given you an angle for the clippers, which when clamped won't move. The clippers can also be rotated with the tube, to get the proper angle to cut the nails.

The base has four pieces. Bottom: 1' x 1' square. Top: 1' x 1' square with 2.5" slots cut down the sides to give space for the nail clippers. Sides: Two 1' x 1' pieces with a 45 degree angle cut beginning 3.5" from the edge of the piece. 

Nail the wood blocks to the bottom, 1/2" from the each edge of the bottom.

Nail each side piece into the sides of the wood blocks.

Glue the top on the angle length on the two side pieces.

Take at least 9 strands of fishing line, 1 m in length, and tie them to the nail clipper. Most nail clippers have a little hole on the clipper handle, which you can slide the line through and knot it. The you run half the strand on each side of the tube clamping the clippers, tha way the line stays in place and pulls on the clipper only regardless of the orientation of the clipper.

Braid the fishing line. 

Drill a hole in the middle of the dowel and run the braid through it. Knot it really well to it won't come undone.

This produces a nice handle that the person can pull to make the clippers close.

Put the mirror and clipper clamps onto the base using bolts and glue. Clamp down the nail clippers and test out the fishing line handle!

Not shown in the image:

Bolts for the clamp rods. Pipe clamp on the clipper tube. Padding on the box. Hockey tape around the clippers. A foot...