Unplug the neon light from its power source.
Cut down the length of the rubber boots that connect the transformer wires to the glass neon tube. Use a utility knife to cut the rubber boots. Be very cautious not to break the glass tube while you cut them off. Peel the boots off the wire and glass tube.
Untwist the wires coming from the transformers from the wires extending out of the glass neon tubes.
Remove the bolts that secure the transformer to the chassis of the neon sign.
Measure the length of the wires on the old transformer and then cut the wires on the new transformer to the same length with wire cutters. Trim an inch of insulation from each wire with wire strippers.
Mount the transformer to the chassis with the original screws. Because you are swapping a solid-state transformer for a new solid-state transformer, use an exact replacement that has the same bolt-hole pattern for mounting.
Cut two 3-inch lengths of shrink tube with your wire cutters.
Slide the shrink tube onto the wires.
Twist the wires on the transformer onto the wires extending from the glass neon tubes.
Slide the shrink tubes halfway onto the glass tubes and then heat the tubing with a lighter to shrink it around the glass and the wires coming from the transformer.