Removing painters tape from vinyl tile

There are a number of adhesive solvents on the market, one of which is named Goo Gone. The "way too long" aspect may result in less than ideal removal rates, however, as the adhesive is like to be excessively dry and may not respond well to the solvent. I expect you'd have ot use a combination of mechanical methods and solvents. The mechanical methods would involve a plastic scraper, not metal, to prevent damage to the tile. A blunt edge as opposed to a sharp one will "snowplow" the old tape and not dig into the tile. Most big box stores and chain hardware stores will carry plastic scrapers. If the ones you find are sharp and not blunt, carefully sand a square edge to it.

You could use a hot air gun, but the temperature control on most models is possibly insufficient. You want to soften the remaining adhesive but not heat the tile in such a way as to damage it. A hair dryer has lower temperatures and may be just the right amount. With the tape "warmed up," it will respond better to the blunt plastic edge.

Another direction involving solvents is to apply the liquid to a rag strip and allow it to soak atop the tape. Using a prickler which looks like a pizza cutter with teeth to puncture the tape may help, but too much pressure will result in tiny dots in the tile, of course.

Extreme conditions would require to construct a series of dams using putty or modeling clay to hold the solvent in place around the tape.

All of the above methods will require varying amounts of elbow grease.