I use the blue painters tape all the time for track and autocross events - it comes in a variety of tack and widths, just look for the most sensitive one. I've never had any issues at all with residue, even after a full track day.
I just ran across this stuff too, but have not yet tried it. I will likely do so in the next few weeks. It's called ISC Surface Guard Tape - Clear Paint Protection Film.
On a side note, I use the "Resuable Vinyl Material" on my coupe for both nubmers and applying sponsor decals. When not at the track, I store the numbers on wax paper - they seem to get about 10-12 events before losing any tack.
Paint Protection
Here is the description from the website:
Surface Guard Tape is a clear protective polyurethane tape that is virtually invisible to the naked eye. Surface Guard will protect any surface that is prone to scratching, chipping, and weathering.
Surface Guard is a semi permanent clear film, with a release liner. 8 Mil Outdoor grade provides excellent protection against ultra violet light, temperature extremes and automotive solvents.
Outdoor grade will not yellow over time.
Be sure to take note that our Surface Guard Tape is made of Polyurethane Material, not PVC or Vinyl. These other types don't conform well, and also cannot, and will not, take the abuse that polyurethane will.
Applications for Surface Guard Tape are endless. From passenger vehicles, bicycles, boats, semis, motorcycles, racecars, RV’s, street rods, snowmobiles, and everything in between, ISC’s Surface Guard can do the job.
Available in either 2" x 12' roll or 4" x 12' roll.
Installation - Click on Image Gallery for Pictures
Surface Guard must be applied to a clean dirt free surface. A heavy duty scissors, knife or blade is necessary to cut Surface Guard. A squeegee should be used to spread out evenly.