Look at the MSDS for your vinyl liquid electrical tape, and you will see what solvent it has in it. Usually some combo of xylene, acetone, and naptha. If your tin is starting to dry out, a small splash of whichever is the major component of its solvent will usually sort it out. Cap it, let it stand overnight then give it a good shake and add a little more solvent if its still too goopy. If its got to the stage of being chunky, you'll probably need to mix solvents to approximate the original solvent mixture and leave it a week or two to redissolve. Its better to under-thin than over-thin, as its easy to add solvent a few drops at a time while stirring to get a good consistency but much more troublesome to have to thicken it up by evaporation while keeping dust out of it.
I've had the same 4 oz can of Optinaut Liquid Electrical Tape on the go for about 20 years. Keep can upright and keep the cap and can screw threads clean and wax or lightly grease the can one so you can get it open again months later. If you know you aren't going to be using it for a while, make sure the lid is fully on and briefly invert it to get a good seal and minimise solvent evaporation.
Unfortunately the rubber liquid electrical tapes actually chemically cure, so once opened have a fairly short life which cant be extended with thinners.